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Dili

Dili (Portuguese and Tetum: Díli) is the capital and largest city of East Timor. It lies on the northern coast of the island of Timor, in a small area of flat land hemmed in by mountains. The climate is tropical, with distinct wet and dry seasons. The city has served as the economic hub and chief port of what is now East Timor since its designation as the capital of Portuguese Timor in 1769. It also serves as the capital of the Dili Municipality, which includes some rural subdivisions in addition to the urban ones that make up the city itself. Dili's growing population is relatively youthful, being mostly of working age. The local language is Tetum; however, residents include many internal migrants from other areas of the country.

The initial settlement was situated in what is now the old quarter in the eastern side of the city. Centuries of Portuguese rule were interrupted in World War II, when Dili became the site of a battle between Allied and Japanese forces. The damaged city returned to Portuguese control following the war. In 1975, a civil war between Timorese political parties broke out, leading to a declaration of independence and a subsequent invasion by Indonesia. Under Indonesian rule infrastructure in the city was developed, with landmarks such as the Immaculate Conception Cathedral and Cristo Rei of Dili being built during this time. The city expanded as its population grew to over 100,000 people.

Resistance to Indonesian rule faced violent repression, and a massacre in Dili led to international pressure culminating in an independence referendum. Following a vote for independence violence erupted in the city, destroying huge amounts of its infrastructure and leading to an exodus of refugees. A period of United Nations rule followed, during which international agencies began the reconstruction of the city. Dili became the capital of an independent East Timor in 2002. A period of violence in 2006 saw another period of infrastructure damage and population displacement. In 2009 the government launched the City of Peace campaign to reduce tensions. As the population has continued to grow and the original site of the city has filled up, the urban area has expanded into coastal areas to the east and west of the main city.

Infrastructure in Dili continues to be developed. The city was the first location in East Timor to see 24 hours of electricity, although its water infrastructure remains relatively limited. Education levels are higher than the national average, and the country's universities are located in the city. An international port and airport lie within the city limits. Most economic activity comes from the tertiary sector and public employment. To further build the economy, the government is developing the tourism potential of the city, focusing on cultural, environmental, and historical attractions.

Initial Portuguese settlement
Dili has played a central role in the history of East Timor. However, early records about Timor, especially before the 1700s, are sparse. The tumultuous history of the city has resulted in a great deal of information being lost; archives in the city were destroyed in 1779, 1890, 1975, and 1999.

The island of Timor was possibly known as a source for sandalwood in the 15th century. The first recorded Portuguese voyage to the island from Portuguese Malacca occurred in 1516, returning with sandalwood. In 1521, sandalwood was left out of a list of products under royal monopoly, leaving most trade with Timor in the hands of private enterprises. Portuguese and Spanish interest in the island increased in the 1520s, with regular trade established by 1524. In the late 1500s, administrative officials began to be appointed to nearby Solor with jurisdiction over that island and Timor, signifying increasing state interest in Portuguese activities there.

The Netherlands began to compete for control of the island in 1613, especially in the west. A rebellion in 1629 forced the Portuguese off the island for three years. In 1641, a number of kings in Timor converted to Catholicism while seeking Portuguese protection. This introduced a political dimension to Portuguese influence, which had previously been primarily economic. Timor became administratively separated from Solor in 1646, although the exact administrative structure is unknown. It received its first dedicated governor in 1702, who resided in Lifau. This reflected the growing importance of Timor compared to nearby Flores. 1749 saw Dutch military forces take control over large portions of the island, broadly reflecting current borders.

In 1769, seeking to break the influence of powerful local families in Lifau, the Portuguese governor António José Teles de Meneses moved the administration and 1,200 people to the site of what would become Dili. It was originally intended that the administration be set up at Vemasse Administrative Post further east, but perhaps because of the favourable geography, a settlement was established at Dili instead. This was at the time part of the Motael kingdom, whose leader was friendly with the Portuguese authorities. The governor occupied an existing fortified structure, and with the assistance of the Motael leader began to construct a new settlement. The area surrounding the settlement was wetlands fed by rivers from the mountains, and proved conducive to rice cultivation. A wall was built to separate the coastal city from wetlands to its south. The initial settlement was divided between three populations, one mainly Portuguese, one of Mestiços and locals from other Portuguese colonies (which became Bidau), and one for troops from a kingdom thought to be in Flores.

From 1788 to 1790, a civil war broke out between the governor in Dili and an official based in Manatuto, which was resolved upon the arrival of a new governor. In response to Dutch provocations, a permanent military force was established in 1818. Some Europeans settled in Lahane to the south, beyond the wetland area. Significant construction was undertaken under governor José Maria Marques, who arrived in 1834 and rebuilt the settlement along a grid. This saw expansion along the coast, but also southwards as the wetlands between the original city and Lahane were channelised and drained. A road extended to Lahane and Dare. The rebuilding saw the settlement being centred on its port, with the immediate port area containing trade facilities, church buildings, military buildings, government buildings, the residence of the governor and his deputy, a residence for a representative of the Motael kingdom, and a residence for the Queen of Manatuto. Of these, only the church and the Finance Deputy's house used masonry. To the east of this core was Bidau and a Chinese settlement, to the west was the main settlement of the Motael kingdom.

In 1844 Timor, along with Macau and Solor, was removed from the jurisdiction of Portuguese India, with the three areas becoming a new Portuguese province. A few years later in 1850, Portuguese Timor was removed from the jurisdiction of the governor of Macau, before being returned to the jurisdiction of Portuguese India in 1856. When English naturalist and explorer Alfred Russel Wallace visited in the 1860s, he wrote that the governor's house was "merely a low whitewashed cottage", and that all other buildings appeared to be mud and thatch. At the time swamps and mudflats surrounded the town, which did not extend to the mountains surrounding it. More permanent buildings of one or two stories were constructed throughout the late 19th century. A new church building was built in 1877.

A revolt to the east led to the city being isolated in 1861; however, the revolt was defeated by the Portuguese and their Timorese allies. In 1863, Dili was declared a city (although the news may not have arrived to the city until the next year), and East Timor became directly subordinate to the Lisbon government. In 1866 the territory was again put under the jurisdiction of Macau. An 1887 mutiny in Dili led to the death of the governor at the time. The territory was separated from Macau for the last time in 1896, again coming directly under the jurisdiction of Lisbon, and becoming a full province in 1909. Another notable revolt took place in the years after the 1910 republican revolution in Portugal. The republican government downgraded the status of its overseas provinces to colonies. A civil government was established in 1913.

Permanent structures in Portuguese style continued to be constructed into the 20th century. A new town hall was built from 1912 to 1915. The main church was demolished in 1933, and a new cathedral opened in its place in 1937. (This cathedral was later destroyed by allied bombing in the Second World War.) Four distinct residential districts developed around the city core. Bidau was the largest, and Benamauc joined it on the eastern side. Caicole developed to the south between the city and Lahane. Colmera developed as a commercial area to the west with a large number of Muslim traders. Motael continued to develop, becoming the site of the city's lighthouse. Motael Church began to be built in 1901. Inland to the southwest, a Chinese cemetery was established, and beyond that a military area known as Taibesse. Lahane also saw significant development in the early 20th century, with its east and west side separated by a river. As the administrative structures developed, Dili became part of the Dili municipality in 1940, the first municipal administration to be created. At the time the municipality was larger, including what is now the Aileu Municipality.

Destruction, reconstruction, and Indonesian rule
During World War II, Portugal and its colonies remained neutral, but the Allies saw East Timor as a potential target for Japanese invasion. Upon the outbreak of the Pacific War in 1941, Australian and Dutch troops were sent to Dili despite Portuguese objections. In response, the Japanese invaded Dili as part of a two-pronged invasion of Timor. The city had been mostly abandoned prior to the invasion, and allied forces retreated further into the island. The Japanese left the Portuguese governor nominally in position, but took over administration. Much of Dili was destroyed during the war, from the initial Japanese invasion and from later allied bombings. Japanese forces on the island of Timor surrendered to Australian forces at the end of the war. Following the surrender, an Australian official travelled to Dili where on 23 September 1945 he informed the Portuguese governor of the Japanese surrender.

Following the Second World War, Dili covered what today is the old core of the city, within the sucos of Acadiru Hun, Bemori, Bidau Lecidere, Caicoli, Colmera, Culu Hun, Gricenfor, Motael, and Santa Cruz. A 1950 census found the municipal population was 442,378, of which 434,907 were considered 'uncilivised' natives. The rest consisted of Chinese, Mestiço, 'civilised' natives, Europeans, and other foreigners such as Goans. Within the urban area of Dili, the population was about 6,000, half 'civilised', and the rest foreigners and mestiços.

Portuguese Timor became a full part of Portugal in 1951, although despite being made citizens of Portugal this did not bring the locals any political power. Following the initial post-war reconstruction of Dili's immediately critical infrastructure, an urban plan was developed in 1951 covering urban layout, road development, zoning, and building regulations. The plan envisioned separate neighbourhoods for Europeans, mestiços, Chinese, Arabs, and Timorese, and assumed there would be further rural-urban migration. Both this plan and later revisions in 1968 and 1972 assumed that the Timorese population would live on the edges of the city yet work near the centre. This plan was not completed, and the city remained under-developed, with low density and where property outside of the central area was still built on with flimsy materials and used for subsistence cultivation. The 1960 census recorded the population of Dili to be about 7,000 people. The second five-year development plan, which ran from 1959 to 1964, saw the reconstruction of the Port of Dili and a small amount of transport infrastructure. The Overseas Organic Law of 1963 created a Legislative Council and extended voting rights to the 'uncivilised'. By 1970, the urban population reached around 17,000. The city did not extend far beyond the area surrounding the port, and the population did not exceed 30,000 before 1975.

The 1974 Carnation Revolution in Portugal created immediate change in East Timor, with new political parties forming with the goal of independence from Portugal. Relationships between these new parties was fractious. Some, particularly the Timorese Democratic Union (UDT), advocated union with Indonesia. On 11 August 1975, the UDT initiated a coup. UDT control was limited outside of Dili, and on 20 August the opposing Fretilin party began its attempt to seize the city. Some houses were set on fire to assist the defence; however, after some days Fretilin succeeded in taking control of the city. The last Portuguese governor fled Dili for Atauro Island on 26 August, as the civil war continued. On 28 November, Fretilin declared independence in a ceremony in Dili. On 7 December, Indonesia landed paratroopers in the city and amphibious forces to its west, as part of an invasion of East Timor, leading many to flee the city.

This invasion brought the territory under Indonesian rule. On 17 July 1976, Indonesia annexed East Timor, which it designated its 27th province. Despite Indonesian attempts to restrict rural-urban migration, the population of Dili continued to grow, reaching 80,000 people in 1985, and over 100,000 in 1999, and economic growth for the territory remained centred in Dili. The city also proved a destination for those fleeing the insurgency in rural areas. Indonesia developed the city's infrastructure, partly as an attempt to win over the population. Structures and monuments built during this time include the Immaculate Conception Cathedral, the Integration Statue commemorating the end of Portuguese rule, and the Cristo Rei of Dili. By the 1990s, urban sprawl had taken up much of the available flat land around the original settlement.

In the 1980s, resistance to Indonesian rule grew among youth in the city. Nonetheless, towards the end of the decade Indonesia began allowing foreign tourists access to the city, with the entire province previously being restricted. A visit by Pope John Paul II in 1989 was interrupted by independence activists. On 12 November 1991, Indonesian forces were filmed shooting at a funeral procession. This led to global condemnation of Indonesia's rule in East Timor, increasing pressure for East Timorese self-determination. The 1997 Asian financial crisis along with a drought related to an El Niño event led to profound food insecurity, worse for Dili than any other city in Indonesia. The crisis also precipitated the resignation of Indonesian President Suharto, whose successor, B. J. Habibie, soon approved a referendum on East Timorese independence. Outbreaks of violence from pro-Indonesian militia occurred throughout the country in the months leading up to the vote. In August 1999, East Timor voted for independence.

The vote led to a period of extreme violence, as pro-Indonesian militia were unchecked by the Indonesian military that was meant to be providing security. On 4 September, when the result was announced, Indonesian police began to leave Dili. In the first 48 hours, international media organisations present in the city reported 145 deaths. Most foreigners were evacuated. Violence continued for several days, causing significant damage to infrastructure and housing in the city. Administrative buildings were looted, and much of the city was destroyed by fire. 120,000 people became refugees. International pressure grew for an international peacekeeping force to replace the Indonesian military, which Indonesia agreed to on 12 September. On 14 September, the UN evacuated refugees that had been sheltering in its Dili compound to Australia. The Australian-led International Force East Timor arrived on 20 September.

Growth under UN rule and independence
Dili continued to grow under UN rule. As Indonesian infrastructure investment outside of Dili was not replicated by the UN government, leaving it to deteriorate, population growth was driven in part due to internal migration from these areas to the city. Housing left abandoned by Indonesians in 1999 was occupied by squatters. This was most common in the western areas of the city. Most inward migration during this period was from eastern areas of the country. Population growth combined with a poor economy led to an increase of urban poverty and unemployment, especially amongst youth. This was despite the city reaping 80% of the economic benefits of reconstruction efforts; 65% of direct jobs created by the UN were in Dili, a figure that rose to 80% when including indirect jobs.

Following the beginning of UN rule, the population of Dili grew by over 10% annually. This was a result of both rural-urban migration, and a baby boom driven by the country having highest fertility rate in the world. By 2004, the population had reached 173,541 people, with unemployment at 26.9% overall, and 43.4% for men aged 15–29. Around half of employment for these young men was informal. In 2005 a new urban master plan was developed by a group based in the Faculty of Architecture of the Technical University of Lisbon. Issues with food security reoccurred periodically throughout the early years of independence. From 1990 to 2014, agricultural use of the flat land around Dili is thought to have decreased by around 40%, replaced by horticulture and aquaculture in the east and by urban areas in the west. Wetlands have also further decreased, drained and built upon.

By 2006, Dili produced half of the country's non-oil GDP. It was also receiving two-thirds of government expenditure, and 80% of goods and services. However, economic benefits were distributed unequally. 1999 saw the end of Indonesian subsidises of core food products, which alongside infrastructure destruction led to rapid inflation. Under UN rule, the use of the US dollar and the purchasing power of international organisations led to price increases. Together, these factors led to extremely high costs of living. Electricity cost four times as much as it did in Indonesia, averaging $15 per household. Telecommunications and petrol similarly grew in price compared to Indonesia. By 2006 Dili had the eighth-highest living costs of any city in Asia, despite the country's having Asia's lowest GDP. At this point, the city had around 300 youth groups, some of which were involved in the informal economy. These groups, driven by unemployment, were often connected to former guerrillas and current politicians. Many developed identities reflecting the regional origins of their members, especially with regards to the broad distinction between those from the east and those from the west.

In April 2006, disputes within the military between a leadership mostly from the east of the country and soldiers mostly from the west spilled over into street violence in Dili. Disputes over housing, again mostly between groups from the east and west, contributed to property destruction. Most of the 150,000 people displaced were from Dili, including about half of the city's residents. Around 72,000 people ended up in camps, while 80,000 fled to rural areas. Rice prices in the city increased by half by October 2006, and then almost doubled again by February 2007. Foreign military intervention was needed to restore order.

A National Recovery Strategy was put in place following the 2007 national election to return these people. In 2008, around 30,000 people displaced from Dili remained in camps, while 70,000 continued to live with friends or family. Continuing unrest led to the attempted assassinations of the country's president and prime minister. By 2009 most displaced people had returned to the city, and the camps were officially closed by the end of the year. However, some community tensions remained. In a couple of areas, there were two or three fights a week between opposing youth groups. Nonetheless, large-scale violence did not return. Mediation teams were utilised to assist in the resettlement of some displaced people to their previous homes.

In May 2009, the year-long Dili City of Peace campaign was launched by Jose Ramos-Horta. The initiative was created to build unity and prevent violence, with the 2006 East Timorese crisis in mind. The campaign included dialogues between different sectors of Timorese society, a cycling tour, a Dili marathon, and a reforestation initiative. Focusing the peace campaign on Dili reflects the influence it has on the entire country, with the government expecting its impacts would extend beyond the city itself. The Latelek (Bridge) Project was instituted from 2010 to 2012 by some organs of the Catholic Church to improve community cohesion, reintegrating previously displaced individuals with those who had remained. Other programs were initiated by the government and NGOs to tackle issues such as skills development, youth engagement, and women's empowerment. Some sucos developed community laws to reduce violence.

By 2010 the municipal population reached 234,026 people, of which 210,250 lived in urban areas. In 2018 the population reached 281,000 people. During a period of COVID-19 restrictions, the city was hit by the worst flood in 50 years in April 2021.

Geography
Dili lies on the northern coast of the island of Timor, which is among the eastern Lesser Sunda Islands and lies in the UTC+9 timezone. Offshore is the Ombai Strait of the Savu Sea,  while to the south is the central mountain range running through Timor. The underlying ground is predominately limestone and marine clay.

The precise location of the city is around 8°35′S, 125°36′E. The city lies mostly within the larger Dili Municipality, whose total area was 367 km2 when including Atauro Island, north of Dili, which was formerly part of the municipality before becoming a separate municipality on 1 January 2022. The municipalities bordering Dili are Aileu, Liquiçá, and Manatuto. The municipality contains 31 sucos, divided into 241 aldeias. The urban area of the city of Dili extends through four of the Dili Municipality's Administrative Posts, Cristo Rei, Dom Aleixo, Nain Feto, and Vera Cruz. 18 sucos within these are considered urban, and this urban area is perhaps 48 km2 large. The wider urban area extends west into the Tibar suco of the Bazartete Administrative Post in the Liquiçá Municipality. The combined area of all sucos within the urban region is 17862 ha, however this includes terrain considered too steep for habitation,  with only perhaps 37%, or 6698 ha, flat enough for development. As of 2014, only 25.5% of the total area was developed.

The main city lies within an area of flat lowlands of less than 100m altitude, mostly between 0 and 60m,  and a slope under 15 degrees. This includes an alluvial plain, and a number of beaches line the coast. The soil underneath this plain is quaternary alluvium. The distance between the sea and the mountains reaches a maximum width of only 4 km, and the surrounding mountains slope near the city at angles of 20 degrees or higher. On either side of the core urban area are mountain ridges extending from the southern range to the coast, leading to urban development spilling over onto areas of flat land on the other sides of these spurs. Tibar lies on the opposite site of the western range, while Hera lies on the opposite side of the eastern range. Another spur encloses Hera on its east.

The Comoro River flows through the western side of the city, while the Bemorl and Benmauc Rivers join together in the East. The Maloa river lies between these. The Maucau river flows through Tibar, while the Akanunu and Mota Kiik rivers flow through Hera. The Comoro is the largest, with a drainage basin extending 9 km inland to a point where the mountains are 900 m high. The water level within these rivers differs greatly between the dry and wet seasons. Parts of the city are considered to face drought hazards and flooding risk from rivers, issues related to climate change. Within the main city of Dili (although not in Hera or Tibar), rivers have reinforced to contain a once-in-25-year flood. Small-scale flooding occurs in a minority of houses a few times each year, and reports of land subsidence are found throughout the city. The Maloa river is the most commonly flooded. Landslides have previously caused damage and loss of life. The area is thought to face earthquake and tsunami risks, although no major events have occurred. Air pollution is considered an increasing issue, with contributors including forest fires, wood-fuelled cooking, and vehicles.

Ecology
The landscape around Dili naturally supports dry deciduous forests. Common tree species there include Sterculia foetida, Callophyllum teysmanii, and Aleurites moluccana. Eucalyptus alba is found in rocky areas, and palm and acacia trees are also found. The eucalyptus trees often serve as firewood, while nuts from A. moluccana are sometimes burnt to produce lighting. Trees found within urban areas include Alstonia scholaris, Albizia julibrissin, Ficus microcarpa, and a variety of fruit trees. While forests around the city have been damaged by harvesting for construction and firewood, the national government aims to reforest these areas. Coral reefs, seagrass meadows, intertidal mudflats, and mangroves can be found along some areas of the coastline. The coral reefs off Dili appear to be locally sheltered from the average sea surface temperature rise from climate change. However, they face some degradation from human activities.

There are three protected biodiversity areas within Dili: Behau, Cristo Rei Protected Area, and Tasitolu. The 18.1 km Cristo Rei Protected Area lies on the mountains separating central Dili and Hera. The 3.8 km Tasitolu area lies near the border of the Dili and Liquiçá municipalities, and covers land and some coastal waters. It is being developed as a recreational site and holy area. The large 274.9 km Behau protected area covers much of the sea off eastern Dili, as well as coastal areas in Hera and to the east. Behau is the most recently proposed of the three areas, and the government is considering abolishing it and replacing it with smaller areas. BirdLife International has identified Cristo Rei Protected Area and Tastitolu as falling within Important Bird Areas. Development can occur in these areas with the approval of the national government.

Climate
Dili has a rather dry tropical savanna climate (Köppen Aw). A rainy season lasts from November to April and a dry season from May to October. Rainfall is highest in December, averaging 170 mm between 2005 and 2013, and lowest in August, averaging 5.3 mm over the same time period. The overall average is 902 mm annually, although there is significant variation between years.

Mean temperatures average around 26 to 28 °C. This changes by 10.8 to 13.8 C-change throughout the day, from minimums at around 20 °C to maximums at over 33 °C. There are larger temperature changes during the dry season. Climate change is shifting weather patterns, and may exacerbate extreme weather events. The highest single recorded temperature in the city up to 2013 was 36 °C in November 2011, while the lowest has been 14 °C in August 2013.

Buildings and monuments
The old quarter of the city lies within what is now the city's eastern half. The original Portuguese settlement occurred in a grid parallel to the shore, and the city has extended along this east-west axis. The older parts of the city are the most densely built up, with little available land. The western portion of the city is the location of the airport and has the most recent urban growth. Most infrastructure was destroyed in 1999,  including 68,000 homes. Following rebuilding as of 2010, 71.6% of houses have concrete or brick walls. In Hera however, just over 50% of houses were mostly wooden as of 2014.

Land rights remain complicated and unresolved as a result of the 2006 crisis, with returns of former residents to the capital having been carried out on an ad-hoc basis. There are disputes between residents who claim land was taken from them by previous regimes, and the national government that has created what is seen as an expansive definition of state land. Developing a formal property system and land register is a key development goal. Those living in houses with this mixed ownership history, perhaps up to 50% of all residents, face heightened risk of eviction.

Important government buildings which form the core of the city are clustered around the Port of Dili. The outskirts of the city are the most recently developed, and grew organically without much urban planning. The central core (Bairro Central) contains most administrative buildings, and has the most buildings constructed with masonry. It retains many buildings that reflect Portuguese-era architecture. To the east of the central government area is the old Chinese area, which still retains a number of Chinese-influenced buildings.

Portuguese-era buildings are most common in the Motael, Gricenfor, and Bidau Lecidere sucos, often stretched along the main road running through the old part of the city, the Avenida Nicolau Lobato. The main government complex is located at the Largo Infante Dom Henrique, next to the seafront. This location was part of the 1951 urban plan. The primary building here is the Government Palace, consists of three two-story buildings connected by a single arcade which were built at different periods between 1953 and 1969. Another old building is the former Market Hall.

The government has identified a number of heritage buildings in the city, especially in the old quarter. New buildings are being built to house cultural institutions. The Museum and Cultural Centre of Timor-Leste is tasked with hosting the country's cultural artefacts. The National Library of East Timor is intended to serve as both a library and a national archive.

Notable churches include the Motael Church, the oldest in the country, which became associated with resistance to Indonesian rule. The Immaculate Conception Cathedral was built with the intention of being the largest church in Southeast Asia. The Cristo Rei of Dili is a 27 m tall statue of Jesus situated on top of a globe at the end of a peninsula in Dili. It is positioned at the end of a Stations of the Cross pathway including over 500 steps. It was a present from the government of Indonesia during occupation for the 20th anniversary of East Timor's integration into Indonesia. Its height reflects the symbolism of East Timor being Indonesia's 27th province at the time of the monument's construction in 1996.

The Integration Monument commemorates the Indonesian annexation of the territory in 1976. It takes the shape of a statue of an East Timorese warrior in traditional dress breaking the chains round his wrists, deliberate chosen to associate traditional Timorese identity with Indonesian rule. The monument has not been demolished, but is instead now regarded as representing the struggle against both periods of foreign rule.

The National Stadium has two seating stands, one on either side, with grass banks providing space for other spectators. It has a capacity of around 9,000 people. It is often used to host association football, the most popular sport in the country, although infrastructure issues mean the national team must sometimes play home games in other countries. In the past it has been used to host refugees and distribute aid.

Administration
Dili is the administrative centre of the Dili Municipality, serving as both the municipal and national capital. The municipality has an elected mayor and council. East Timor's municipalities are divided into administrative posts, and each of these is divided into sucos. The central city of Dili is spread over four of the six administrative posts within Dili municipality: Cristo Rei, Dom Aleixo, Nain Feto, and Vera Cruz. The Hera suco is the easternmost suco of Cristo Rei. Tibar, to the west of the main city, is the easternmost suco of the Bazartete Administrative Post in the Liquiçá Municipality.

Each suco has a chefe. Those in Dili have less influence over community land than those elsewhere, however their elected status gives them greater authority in other areas. Each also has a head office. Municipal and national government buildings are concentrated in the city centre, mainly in the sucos of Caicori, Colmera, and Gricenfor. Sucos, administrative posts, and municipalities are all tasked with setting up a Disaster Management Committee. These are responsible for planning, public awareness, and disaster response. The borders of sucos, and the aldeias within them, are often undefined. Reasons for this include the history of displacement, and taboo over formal demarcation.

Land registration is difficult due to the city's tumultuous history, and legal ownership is often unclear. It is thought that in 1999 existing land records were taken from Dili to Indonesia. The new government attempted to set up a system of rent, charging a small fee of $10 a month for those occupying state property. However, in many cases even this could not be paid. In 2003 the national government legislated that all previous state property, as well as abandoned properties, belonged to the state. It also set up a system of registration based on occupation. Residents can claim land they live in, if there are no objections from others. The 2006 crisis put an end to attempts to enforce rent. Evictions from state property are rare. A cadastral survey began in 2008. As of 2014, 70% of the land in Dili had been surveyed, although this information is not public. Despite this lack of information, most in the city claim ownership of their homes, with 90% of homes considered owned by an individual or by a family. Land valuation is often unclear.

The sucos within the four administrative posts in the Dili Municipality are as follows:

Cristo Rei
 * Balibar
 * Becora
 * Bidau Santana
 * Camea
 * Culu Hun
 * Hera
 * Meti Aut

Dom Aleixo
 * Bairropite
 * Comoro
 * Fatuhada
 * Kampung Alor

Nain Feto
 * Acadiru Hun
 * Bemori
 * Bidau Lecidere
 * Gricenfor
 * Lahane Oriental
 * Santa Cruz

Vera Cruz
 * Caicoli
 * Colmera
 * Dare
 * Lahane Ocidental
 * Mascarenhas
 * Motael
 * Vila Verde

Economy
The economic situation in Dili is substantially better than that of the rest of the country, and most wealth is concentrated there. Almost all of the sucos of Dili are among those with the country's highest living standards and the greatest access to public services. The Dili district as a whole has a higher significantly higher living standard than any other part of the country, and while poverty rates within the sucos of the municipality as a whole range from 8 to 80%, every suco within the city proper was ranked within the highest level of living standards. 57.8% of those in the capital are among those with relatively high levels of wealth, as opposed to 8.7% in rural areas.

In 2004 18,331 people were working in the agricultural sector, 1,885 in resources and manufacturing, 5,027 in hospitality, 3,183 in finance, real estate, and logistics, 6,520 in government services and security, 879 in home industries, 6,354 for international diplomatic bodies, and 2,142 unknown. By 2010, the tertiary sector employed 44% of those working, with government employment providing around 25% of jobs. The primary sector is slightly smaller than the government in terms of employment, while the secondary sector remains small. The working age population grew by almost 50% from 2004 to 2010, while unemployment declined from 26.9% to 17.4%. Nonetheless, youth unemployment in the municipality stood at 58% in 2007, above the national average of 43%. The capital attracts younger and educated individuals from the rest of the country. The city lies within what the government calls the "Northern Regional Development Corridor", which stretches along the coast from the Indonesia border to Baucau. Within this, it is part of the smaller "Dili-Tibar-Hera" area in which the government plans to develop the service sector. The city is also part of what is designated the central tourism zone. Sites related to important historical events are promoted, as well as eco-tourism. Whale watching is possible off the coast,  and there are many scuba diving sites near the city. Some tourism and industrial complexes are being developed within the metropolitan area. There is a large informal economy that includes some of the officially unemployed residents.

Tourism numbers increased from 14,000 to 51,000 from 2006 to 2013. Half of visitors arriving at Dili's airport come from three countries: Australia, Indonesia, and Portugal. Near the beginning of UN rule, there were at least 9 hotels with 550 rooms. As of 2012, there were at least 14 hotels in the city. Most hotels are run by local companies, with few international chains present. Nightly rates are relatively high for the region, partially due to a lack of sufficient tourists to benefit from economies of scale. Important hotels include Hotel Timor and Hotel Dili.

Most large investments come from the public sector, although there is a growing small-scale private sector. The Dili municipality is responsible for around 40% of the country's fish production, most of which is consumed domestically. The country's three significant commercial banks operate primarily in Dili.

The Port of Dili is the country's largest. It handles the majority of international shipping. There are regular ships to Darwin (Australia), Kota Kinabalu (Malaysia), Surabaya (Indonesia), and Singapore, and less frequent shipping to and from other Indonesian ports. As of 2011, the port processed 200,000 tonnes of goods annually, which had increased by 20% each year for the previous six years. 80% of the goods processed are imports.

Demographics

In 2004, the number of dwellings in Dili Municipality was 26,114, while the number of households was 31,702. The population increased from 175,730 to 234,331 between 2004 and 2010, while the average household size increased from 5.5 to 6.7. The gender ratio was 51% male to 49% female. The 2010 census recorded a population of 193,563 in the areas of Dili district classified as urban, with a population of 234,331 in the whole district including rural areas such as Atauro and Metinaro. Within the Dili metropolitan area, the total population was 223,793 as of 2010, containing 33,163 households with an average size of 6.7. The gender ratio is slightly more unbalanced, with 53% male and 47% female. The population density is about 33.4 people per hectare within the metropolitan area's habitable land. It is higher in areas of unplanned settlement than in planned neighbourhoods. The most populous of the administrative posts is Dom Aleixo, which by itself contained 105,154 people in 2010.

Between 2001 and 2004, the population of Dili Municipality grew by 12.58%, with only 54% of the district's inhabitants born in the city. 7% were born in Baucau, 5% each in Viqueque and Bobonaro 4% in Ermera, and the remainder in other districts or overseas. The population growth of the Dili Municipality from 2004 to 2010 represented 40% of the country's total population growth, and is driven in part by internal migration, especially that of younger people. Net migration into the municipality during this period was 24,000 people. Due to limited space, a small number of people settled in hilly and mountainous areas starting around 1990, especially in southern areas near the national highway. However, due to properties being abandoned following the independence vote, much settlement in the 21st century has been into these vacated areas. The working age population, those aged 15 to 64, made up 63% of residents in the metropolitan area in 2010. Many of these people were under 29.

The 2022 census found the population of the municipality increased to 324,269, of which 95.8% were urban. The municipality had the highest growth rate in the country since 2015, although average household size decreased from 6.4 to 5.7. The municipality is the most densely populated in the country, and Dom Aleixo with 166 thousand people remained the most populous administrative post. By 2030, the population of the municipality is predicted to reach around 580,000.

The primary local language is Tetum, which was promoted during Portuguese rule and has become an official language of the country. Speakers from the other languages of East Timor are present in the city, where the official language of Portuguese and the working languages of English and Indonesian are also spoken. A dialect of Malay-based creole called Dili Malay is spoken by perhaps 1,000 residents with ancestral links to Alor Island. Migration into the city has led to clustering of incoming migrants into areas with others of similar backgrounds.

Education
Education is more common in Dili Municipality than elsewhere in the country. The attendance rate at primary schools increased from 37% in 2004 to 73% in 2010. As of 2010, 86% of those five or older in the municipality had attended primary school, equivalent to the literacy rate. Within the metropolitan area, education rates are highest in Nain Feto and Vera Cruz, where 88% are either attending or have attended primary school. These are followed by Dom Alexio at 87%, and Cristo Rei at 81%. Tibar, lying outside of Dili Municipality, has the lowest at 75%.

As of 2013, there were 108 schools in Dili, Hera, and Tibar, including primary, secondary, and specialist schools. Of these, 61 were public and 47 private. This equated to 4.8 schools per 10,000 people. In 2011, 43% of students in the Dili municipality studied in private schools. Many private schools are run by the Catholic Church, for example, Don Bosco Training Center, including 32% of all schools in the Dili Municipality.

Seventy-six per cent of the country's university students study in the municipality. This is responsible for some of the internal migration to the city. The National University of East Timor created a "University City" master plan to develop the Hera area.

Infrastructure

Up to 70% of the country's infrastructure was destroyed in 1999, including almost the entire electrical grid, and much of the water infrastructure. Dili's airport and port were rehabilitated in the six years following this, along with electricity and telecommunications. The rapid population growth of the city has put a strain on some of its infrastructure services. Pre-independence laws prohibiting building within 100 m of water bodies are not enforced, with population growth leading to structures such as housing being built in flood-prone areas, including along dry river beds and canals.

Electricity
In the early years of UN rule, electricity was provided by the Comoro power station, which has a 16 MW diesel generator. By 2004, there were 23,000 connections in the city creating a demand of 12.5 MW. At the time, Dili was the only location in East Timor with 24-hour electricity. Electricity demand peaked from 19:00 to 22:00. By 2009, Comoro was producing 32 MW, and by the year after that 92.3% of Dili's households used electricity for lighting purposes. Cooking remained carried out using firewood by 66.2% of households, with electricity being used by just 10.1%. Non-payment of electricity bills has caused some funding problems. In 2011, only 40% of commercial recipients of electricity paid their electricity bills.

In November 2011, the diesel generators at the new Hera Power Station became operational, producing 119 MW. This replaced the operations of the Comoro station, with Hera able to produce electricity using 17% less fuel. A new substation was created to supply Dili, and transmission lines link Dili to other cities and towns along the northern coast, part of a ring surrounding the country. As of 2016, Dili's peak power demand reached 42.11 MW. The development of electricity infrastructure since independence has significantly reduced electricity costs, which moved from 249c per kilowatt-hour in 2002 to 5c per kilowatt-hour in 2014.

Telecommunications
Most telecommunication activity in the country is carried out using mobile phones. Most of the only 3000 landlines are found in Dili. There are no submarine communications cables connecting to the country, so internet access is supplied via satellites. This is expensive, and internet usage nationally was only just above 1% in 2016. The government has approved the installation of the Timor-Leste South submarine Cable (TLSSC), connecting to Darwin in Australia, as well as another cable connecting to the Indonesian island of Alor. As of 2020, there were 3 telecommunications companies in the country.

Water and sanitation
Access to clean water and sanitation is an issue for some households. Over $250 million was invested by the UN and other organisations to build Dili's water infrastructure. Existing water sources and transportation infrastructure are considered sufficient to meet the immediate needs of the city, although work continues to improve quality and reliability. In 2007, 25% of residents received 24 hours of water. As of 2013, while 36% of households were connected to the water supply system, half Dili received less than six hours of water a day. Furthermore, water quality was irregular, with boiling advised. By 2015, it remained the case that less than 30% of those in Dili had access to a continuous water supply. In 2018, water remained available on average from 4 to 8 hours.

Water is managed by the National Directorate of Water and Sanitation Services (Dirasaun Nasional Sistema Agua no Saneamentu/DNSAS), which derives 60% of water supplies from groundwater. This groundwater extraction began in the 1980s, and accelerated after independence. Private entities also pump water from the aquifer without regulation. Despite the inconsistency of supply, 91% of those in urban areas have some access to safe drinking water, with sources including pumps, public taps, and wells and boreholes. Some households have tanks installed to alleviate the impact of service interruptions. Half of the city's water comes from a local aquifer, and there are four water treatment plants at the southern edges of the city. Water tariffs were put in place in 2004, but were removed in 2006 following the 2006 East Timorese crisis. By 2010 27.821 m3 of water was pumped from the aquifer each day, almost as fast as the aquifer could refill. Trials for water tariff re-introduction began in 2013. Increasing usage has led to the aquifer, the Dili Groundwater Basin, being unable to match demand during the dry season. An increasing number of wells has increased demand, while development altering drainage patterns has limited recharge rates. The aquifer is constrained by the ocean on one side and mountains on the others. Downstream areas also face saltwater intrusion.

Dili is the location of the country's water testing laboratory, and thus its water quality is regularly monitored. The lack of manufacturing in the city is thought to have limited potential water pollution. However, pollution risks emerge from the common discharge of untreated household water, and leakage from latrine pits into the soil  and relatively high water table. Water stores in households, as well as from some wells, has been found to have bacteriological contamination. As of 2010, only 16% of households emptied their latrine pits. Hera and Tibar lack water treatment plants, with residents relying on boreholes and delivery by water trucks. As of 2010, daily demand was 32,000 m3 in Dili proper, 520 m3 in Hera, and 220 m3 in Tibar.

Drainage infrastructure is insufficient to handle the wet season, with drains often being blocked and resultant flooding being common. This creates property damage and health concerns. Thirty-six water channels lie within the city in addition to its rivers. These often collect rainwater; however, the growing urbanisation of the city is reducing infiltration capacity, worsening flood risks. There is no city-wide sewerage system. As of 2010, only 30.3% of households had access to a sceptic tank. The most common sewage disposal system was pit latrines, which were used by 50.7% of households. Among households with toilets, 97% were flushed through the manual pouring of water. Wastewater is often collected from some areas by trucks. Some wastewater is treated in ponds in Tasitolu. Dili also has one of the country's two septage treatment facilities. A Sanitation and Drainage Masterplan was created for the city in 2012, envisioning the creation of eight wastewater treatment systems in the city by 2025.

As of 2014, Dili produces 108 tons of solid waste per day, over half of which is biodegradable. The government-funded waste collection system covers Cristo Rei, Dom Aleixo, Nain Feto, and Vera Cruz, with waste being collected by a mixture of government trucks and private trucks contracted by the government. Collected waste is disposed in a landfill in Tibar, which was established during the Indonesian period. Metal collected by waste pickers is sold to Malaysia and Singapore for recycling, while some biodegradable waste is composted by a private company. Some waste is burnt. Waste collection schedules are variable, with some areas receiving daily collection and some receiving none. Collection is less frequent in Hera and Tibar than in Dili proper.

There are 14 hospitals around the Dili metropolitan area, nine in Dom Aleixo, three in Vera Cruz, one in Cristo Rei (in Hera), and one in Tibar. Dom Aleixo also has two health centres, with Cristo Rei having one health centre in Dili proper, and Nain Feto also having a health centre. The National Hospital of Timor-Leste is located in Dili, catering to primary and secondary health care. A specialist hospital is planned to be constructed by 2030 to deal with diseases, such as cancer, that are currently treated outside of the country.

Land
As of 2015, Dili Municipality had 1475 km of roads, of which half was classified as National, District, or Urban. The roads heading into and out of Dili to the East and West carry over 1,000 non-motorbike vehicles daily. In addition to the Eastern and Western national roads, a third national road extends south from the city. Within Dili, there is rising congestion. Poor road quality is the most common cause of accidents and delays. Many roads are unpaved, and within the old quarter, streets are often one-way. The only four lane roads in the city are National Road A01 and Banana Road. As of 2016, there were four roundabouts and 11 intersections with traffic lights. Few routes travel along the east-west axis, and for most of the time since independence there was only one vehicular crossing across the Comoro river. This bridge was expanded from two lanes to four lanes in June 2013. The two-lane Hinode Bridge was opened upriver in September 2018, connecting Banana road to National Road No 03. It is expected that this bridge will also be expanded to four lanes in the future.

The usual form of public transportation within the city is the minibus, which are operated by private companies that purchase route franchises from the government. Each vehicle usually has a capacity of ten people. There are no formal schedules and few official bus stops. Fares are cheap, at $0.25. Dili is also served by a fleet of air-conditioned blue taxis, whose drivers are expected to speak Tetum and English.

Street names are in Portuguese, as are many official signs labelling locations. Tetum is used for more informational signage. English and Indonesian are rare in official signage, but are more common elsewhere. Chinese is used on some informal signage, while non-Tetum Timorese languages are not used. Even under Indonesian rule, during which the use of Portuguese was banned, Portuguese street names like Avenida Marechal Carmona remained unchanged, although they were prefixed with the Indonesian word Jalan or 'road'.

Sea
The Port of Dili has a total berth length of 289.2 m. Depths alongside the berth range from 5.5 m to 7.5 m. This port was previously the only international cargo reception port in the country, but its capacity is insufficient to meet import needs. The Tibar Bay Port was thus planned to handle all cargo shipping, leaving the current Dili port to become a dedicated ferry terminal. Tibar Bay Port was expected to be built starting in 2015, and scheduled for opening in 2020. On 3 June 2016 the government signed a Public-private partnership agreement with Bolloré, giving the company a 30-year least on the new port. A construction tender was awarded to the China Harbour Engineering Company in December 2017. Construction began on 30 August 2019, with completion scheduled for August 2021. As of December 2020 construction was 42% complete, with delays including Chinese workers returning to China during the COVID-19 pandemic. The port was then expected to open in April 2022. The port received its first ships on 30 September that year, and was officially inaugurated on 30 November 2022.

A dry port has been created 8 km from the main Port of Dili, and there is a naval port in Hera. Cargo operations in Dili Port halted from 1 October 2022. A twice-weekly ferry service operates between Dili and Oecusse, and a ferry travels between Dili and Atauro once a week. The Dili Port serves as the main link for these locations with the rest of the country. These ferries deposit people and vehicles onto a slipway, rather than a dedicated berthing.

Air
The Presidente Nicolau Lobato International Airport, named after independence leader Nicolau Lobato, is located in the city. It serves regular flights to Darwin (Australia), Denpasar (Indonesia), and Singapore. In 2014, it served 198,080 passengers and 172 tons of cargo. It has one runway, which is 1850 m long and 30 m wide, lying 8 m above mean sea level. A lack of runway lighting prevents night-time landings, so the airport operates from 6 am to 6 pm. The passenger terminals were originally domestic terminals during the Indonesian period, leaving them ill-designed to handle international customs and immigration. Due to the size of the runway, only medium-sized planes such as the A310 and the B737 can be accommodated, and there is limited space for aircraft parking. The runway is constrained by the sea and the Comoro river, although there are plans to extend the runway through land reclamation and/or by bridging the river. A new international terminal is also planned. Despite this, it is thought the airport may be able to handle capacity requirement until 2030.

This is the only functioning international airport in East Timor, though there are airstrips in Baucau, Suai and Oecusse used for domestic flights. Until recently, Dili's airport runway has been unable to accommodate aircraft larger than the Boeing 737 or C-130 Hercules, but in January 2008, the Portuguese charter airline EuroAtlantic Airways operated a direct flight from Lisbon using a Boeing 757, carrying 140 members of the Guarda Nacional Republicana.

Culture
The national government has crafted a culture policy that includes the provision of cultural facilities in Dili and aims to have the city reflect diverse cultural influences. The development of cultural facilities has included the building up of cultural institutions such as libraries and museums, and the development of audio-visual multimedia centres through which information will be more accessible. The "City of Peace" marathon was first held in June 2010, following which it became an annual event. It includes a full marathon, a half marathon, and a seven-kilometre run.

Within the city, cultural difference exist not only between different ethnolinguistic groups, but between more established residents of the city, and recent immigrants who retain different cultural practices. Legal traditions reflecting Portuguese and Indonesian rule do not always align with customary practices, such as in the recognition of marriages. Those who migrate internally into Dili retain cultural and identity links to their rural areas of origin, which are passed down through generations. Urban residents often return to rural areas for traditional ceremonies, especially during the dry season, and elections.

As in the rest of the country, village chiefs continue to have some influence in Dili's communities. Local communities have important traditional houses, as well as sacred natural areas including specific trees and rocks. However, with suco populations being more diverse in Dili than in rural areas, suco chief power is not as established or effective. Community links are instead more common at aldeia levels, or even established through religious or economic links instead. New arrivals often settle near those from the same area of origin, leading Dili's urban population to have formed into a patchwork of different communities. Migration back and forth from Dili to rural areas is not uncommon. Furthermore, while rural sucos are often somewhat culturally homogenous and linked by family relationship, these administrative boundaries do not map with the cultural settlement patterns of modern Dili.

There is some more homogeneity at the aldeia level due to families settling near relatives, although this is also not consistent. Aldeia nearer the outskirts, or in areas formerly populated by Indonesian civil servants, are both more densely populated and particularly heterogenous both ethnolinguistically and socioeconomically. In diverse aldeias, smaller communities sometimes develop with their own informal leadership. Some urban areas exhibit occupational or status-based segregation. Core urban areas are dominated by relatively wealthy families, often those that were considered mestiços or assimilados under Portuguese rule. Some aldeias mostly consist of those of foreign descent, or of transient students.

Dili contains a number of local and often youth collectivities. While sometimes described as gangs, many function more as social collectivities integrated into their local community. Such groups have a long history, many forming as an act of resistance against Indonesian rule. Some street art continues to reflect a theme of resistance. The composition of these groups often reflects areas of rural origin, and the broader East-West divide that exists within the country.

Dili had no cinema as of 2011. In 2019, the city hosted the first Dili International Film Festival, which was repeated in 2020. Radio is very popular, and the city has 13 FM radio stations.

Embassies

 * 🇦🇺 australia
 * 🇧🇷 brazil
 * undefined
 * 🇨🇳 china
 * 🇨🇺 cuba
 * 🇮🇩 indonesia
 * 🇯🇵 japan

 * 🇰🇷 south korea
 * 🇲🇾 malaysia
 * 🇳🇿 new zealand
 * 🇵🇭 philippines
 * 🇵🇹 portugal
 * 🇹🇭 thailand
 * 🇺🇸 united states

Twin towns – sister cities
Dili is twinned with the following places:

title: Dili


text:
Urysohn's lemma

In topology, Urysohn's lemma is a lemma that states that a topological space is normal if and only if any two disjoint closed subsets can be separated by a continuous function.

Urysohn's lemma is commonly used to construct continuous functions with various properties on normal spaces. It is widely applicable since all metric spaces and all compact Hausdorff spaces are normal. The lemma is generalised by (and usually used in the proof of) the Tietze extension theorem.

The lemma is named after the mathematician Pavel Samuilovich Urysohn.

Discussion
Two subsets $$A$$ and $$B$$ of a topological space $$X$$ are said to be separated by neighbourhoods if there are neighbourhoods $$U$$ of $$A$$ and $$V$$ of $$B$$ that are disjoint. In particular $$A$$ and $$B$$ are necessarily disjoint.

Two plain subsets $$A$$ and $$B$$ are said to be separated by a continuous function if there exists a continuous function $$f : X \to [0, 1]$$ from $$X$$ into the unit interval $$[0, 1]$$ such that $$f(a) = 0$$ for all $$a \in A$$ and $$f(b) = 1$$ for all $$b \in B.$$ Any such function is called a Urysohn function for $$A$$ and $$B.$$ In particular $$A$$ and $$B$$ are necessarily disjoint.

It follows that if two subsets $$A$$ and $$B$$ are separated by a function then so are their closures. Also it follows that if two subsets $$A$$ and $$B$$ are separated by a function then $$A$$ and $$B$$ are separated by neighbourhoods.

A normal space is a topological space in which any two disjoint closed sets can be separated by neighbourhoods. Urysohn's lemma states that a topological space is normal if and only if any two disjoint closed sets can be separated by a continuous function.

The sets $$A$$ and $$B$$ need not be precisely separated by $f$, i.e., it is not necessary and guaranteed that $$f(x) \neq 0$$ and $$\neq 1$$ for $$x$$ outside $$A$$ and $$B.$$ A topological space $$X$$ in which every two disjoint closed subsets $$A$$ and $$B$$ are precisely separated by a continuous function is perfectly normal.

Urysohn's lemma has led to the formulation of other topological properties such as the 'Tychonoff property' and 'completely Hausdorff spaces'. For example, a corollary of the lemma is that normal T1 spaces are Tychonoff.

Formal statement
A topological space $$X$$ is normal if and only if, for any two non-empty closed disjoint subsets $$A$$ and $$B$$ of $$X,$$ there exists a continuous map $$f : X \to [0, 1]$$ such that $$f(A) = \{ 0 \}$$ and $$f(B) = \{ 1 \}.$$

Proof sketch
The proof proceeds by repeatedly applying the following alternate characterization of normality. If $$X$$ is a normal space, $$Z$$ is an open subset of $$X$$, and $$Y\subseteq Z$$ is closed, then there exists an open $$U$$ and a closed $$V$$ such that $$Y\subseteq U\subseteq V\subseteq Z$$.

Let $$A$$ and $$B$$ be disjoint closed subsets of $$X$$. The main idea of the proof is to repeatedly apply this characterization of normality to $$A$$ and $$B^\complement$$, continuing with the new sets built on every step.

The sets we build are indexed by dyadic fractions. For every dyadic fraction $$r \in (0, 1)$$, we construct an open subset $$U(r)$$ and a closed subset $$V(r)$$ of $$X$$ such that: Intuitively, the sets $$U(r)$$ and $$V(r)$$ expand outwards in layers from $$A$$:
 * $$A \subseteq U(r)$$ and $$V(r)\subseteq B^\complement$$ for all $$r$$,
 * $$U(r)\subseteq V(r)$$ for all $$r$$,
 * For $$r < s$$, $$V(r)\subseteq U(s)$$.

 * $$\begin{array}{ccccccccccccccc}

A&&&&&&&\subseteq&&&&&&& B^\complement\\ A&&&\subseteq&&&\ U(1/2)&\subseteq& V(1/2)&&&\subseteq&&& B^\complement\\ A&\subseteq& U(1/4)&\subseteq& V(1/4)&\subseteq& U(1/2)&\subseteq& V(1/2)&\subseteq& U(3/4)&\subseteq& V(3/4)&\subseteq& B^\complement \end{array}$$

This construction proceeds by mathematical induction. For the base step, we define two extra sets $$U(1) = B^\complement$$ and $$V(0) = A $$.

Now assume that $$n \geq 0$$ and that the sets $$U\left(k/2^n\right)$$ and $$V\left(k/2^n\right)$$ have already been constructed for $$k \in\{ 1, \ldots, 2^n - 1\}$$. Note that this is vacuously satisfied for $$n=0$$. Since $$X$$ is normal, for any $$a \in \left\{ 0, 1, \ldots, 2^n - 1 \right\}$$, we can find an open set and a closed set such that

 * $$V\left(\frac{a}{2^n}\right)\subseteq U\left(\frac{2a+1}{2^{n+1}}\right)\subseteq V\left(\frac{2a+1}{2^{n+1}}\right)\subseteq U\left(\frac{a+1}{2^n}\right)$$

The above three conditions are then verified.

Once we have these sets, we define $$f(x) = 1$$ if $$x \not\in U(r)$$ for any $$r$$; otherwise $$f(x) = \inf \{ r : x \in U(r) \}$$ for every $$x \in X$$, where $$\inf$$ denotes the infimum. Using the fact that the dyadic rationals are dense, it is then not too hard to show that $$f$$ is continuous and has the property $$f(A) \subseteq \{ 0 \}$$ and $$f(B) \subseteq \{ 1 \}.$$ This step requires the $$V(r)$$ sets in order to work.

The Mizar project has completely formalised and automatically checked a proof of Urysohn's lemma in the URYSOHN3 file.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Urysohn's lemma


text:
Talk:Irina Privalova

inaccurate results in body copy
says she won a medal in the 200m in 1992 - she did not. she won a medal in the 100 and in the relay. — Preceding unsigned comment added by 118.211.216.247 (talk) 11:48, 9 October 2016 (UTC)

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Age of Earth

The age of Earth is estimated to be 4.54 ± 0.05 billion years (4.54 × 109 years ± 1%). This age may represent the age of Earth's accretion, or core formation, or of the material from which Earth formed. This dating is based on evidence from radiometric age-dating of meteorite material and is consistent with the radiometric ages of the oldest-known terrestrial material and lunar samples.

Following the development of radiometric age-dating in the early 20th century, measurements of lead in uranium-rich minerals showed that some were in excess of a billion years old. The oldest such minerals analyzed to date—small crystals of zircon from the Jack Hills of Western Australia—are at least 4.404 billion years old. Calcium–aluminium-rich inclusions—the oldest known solid constituents within meteorites that are formed within the Solar System—are 4.567 billion years old, giving a lower limit for the age of the Solar System.

It is hypothesised that the accretion of Earth began soon after the formation of the calcium-aluminium-rich inclusions and the meteorites. Because the time this accretion process took is not yet known, and predictions from different accretion models range from a few million up to about 100 million years, the difference between the age of Earth and of the oldest rocks is difficult to determine. It is also difficult to determine the exact age of the oldest rocks on Earth, exposed at the surface, as they are aggregates of minerals of possibly different ages.

Development of modern geologic concepts
Studies of strata—the layering of rocks and soil—gave naturalists an appreciation that Earth may have been through many changes during its existence. These layers often contained fossilized remains of unknown creatures, leading some to interpret a progression of organisms from layer to layer.

Nicolas Steno in the 17th century was one of the first naturalists to appreciate the connection between fossil remains and strata. His observations led him to formulate important stratigraphic concepts (i.e., the "law of superposition" and the "principle of original horizontality"). In the 1790s, William Smith hypothesized that if two layers of rock at widely differing locations contained similar fossils, then it was very plausible that the layers were the same age. Smith's nephew and student, John Phillips, later calculated by such means that Earth was about 96 million years old.

In the mid-18th century, the naturalist Mikhail Lomonosov suggested that Earth had been created separately from, and several hundred thousand years before, the rest of the universe. Lomonosov's ideas were mostly speculative. In 1779 the Comte du Buffon tried to obtain a value for the age of Earth using an experiment: he created a small globe that resembled Earth in composition and then measured its rate of cooling. This led him to estimate that Earth was about 75,000 years old.

Other naturalists used these hypotheses to construct a history of Earth, though their timelines were inexact as they did not know how long it took to lay down stratigraphic layers. In 1830, geologist Charles Lyell, developing ideas found in James Hutton's works, popularized the concept that the features of Earth were in perpetual change, eroding and reforming continuously, and the rate of this change was roughly constant. This was a challenge to the traditional view, which saw the history of Earth as dominated by intermittent catastrophes. Many naturalists were influenced by Lyell to become "uniformitarians" who believed that changes were constant and uniform.

Early calculations
In 1862, the physicist William Thomson, 1st Baron Kelvin published calculations that fixed the age of Earth at between 20 million and 400 million years. He assumed that Earth had formed as a completely molten object, and determined the amount of time it would take for the near-surface temperature gradient to decrease to its present value. His calculations did not account for heat produced via radioactive decay (a then unknown process) or, more significantly, convection inside Earth, which allows the temperature in the upper mantle to remain high much longer, maintaining a high thermal gradient in the crust much longer. Even more constraining were Thomson's estimates of the age of the Sun, which were based on estimates of its thermal output and a theory that the Sun obtains its energy from gravitational collapse; Thomson estimated that the Sun is about 20 million years old.

Geologists such as Lyell had difficulty accepting such a short age for Earth. For biologists, even 100 million years seemed much too short to be plausible. In Charles Darwin's theory of evolution, the process of random heritable variation with cumulative selection requires great durations of time, and Darwin stated that Thomson's estimates did not appear to provide enough time. According to modern biology, the total evolutionary history from the beginning of life to today has taken place since 3.5 to 3.8 billion years ago, the amount of time which passed since the last universal ancestor of all living organisms as shown by geological dating.

In a lecture in 1869, Darwin's great advocate, Thomas Henry Huxley, attacked Thomson's calculations, suggesting they appeared precise in themselves but were based on faulty assumptions. The physicist Hermann von Helmholtz (in 1856) and astronomer Simon Newcomb (in 1892) contributed their own calculations of 22 and 18 million years, respectively, to the debate: they independently calculated the amount of time it would take for the Sun to condense down to its current diameter and brightness from the nebula of gas and dust from which it was born. Their values were consistent with Thomson's calculations. However, they assumed that the Sun was only glowing from the heat of its gravitational contraction. The process of solar nuclear fusion was not yet known to science.

In 1892, Thomson was ennobled as Lord Kelvin in appreciation of his many scientific accomplishments. In 1895 John Perry challenged Kelvin's figure on the basis of his assumptions on conductivity, and Oliver Heaviside entered the dialogue, considering it "a vehicle to display the ability of his operator method to solve problems of astonishing complexity." Other scientists backed up Kelvin's figures. Darwin's son, the astronomer George H. Darwin, proposed that Earth and Moon had broken apart in their early days when they were both molten. He calculated the amount of time it would have taken for tidal friction to give Earth its current 24-hour day. His value of 56 million years was additional evidence that Thomson was on the right track. The last estimate Kelvin gave, in 1897, was: "that it was more than 20 and less than 40 million year old, and probably much nearer 20 than 40". In 1899 and 1900, John Joly calculated the rate at which the oceans should have accumulated salt from erosion processes and determined that the oceans were about 80 to 100 million years old.

Overview
By their chemical nature, rock minerals contain certain elements and not others; but in rocks containing radioactive isotopes, the process of radioactive decay generates exotic elements over time. By measuring the concentration of the stable end product of the decay, coupled with knowledge of the half life and initial concentration of the decaying element, the age of the rock can be calculated. Typical radioactive end products are argon from decay of potassium-40, and lead from decay of uranium and thorium. If the rock becomes molten, as happens in Earth's mantle, such nonradioactive end products typically escape or are redistributed. Thus the age of the oldest terrestrial rock gives a minimum for the age of Earth, assuming that no rock has been intact for longer than Earth itself.

Convective mantle and radioactivity
The discovery of radioactivity introduced another factor in the calculation. After Henri Becquerel's initial discovery in 1896,   Marie and Pierre Curie discovered the radioactive elements polonium and radium in 1898; and in 1903, Pierre Curie and Albert Laborde announced that radium produces enough heat to melt its own weight in ice in less than an hour. Geologists quickly realized that this upset the assumptions underlying most calculations of the age of Earth. These had assumed that the original heat of Earth and the Sun had dissipated steadily into space, but radioactive decay meant that this heat had been continually replenished. George Darwin and John Joly were the first to point this out, in 1903.

Invention of radiometric dating
Radioactivity, which had overthrown the old calculations, yielded a bonus by providing a basis for new calculations, in the form of radiometric dating. Ernest Rutherford and Frederick Soddy jointly had continued their work on radioactive materials and concluded that radioactivity was caused by a spontaneous transmutation of atomic elements. In radioactive decay, an element breaks down into another, lighter element, releasing alpha, beta, or gamma radiation in the process. They also determined that a particular isotope of a radioactive element decays into another element at a distinctive rate. This rate is given in terms of a "half-life", or the amount of time it takes half of a mass of that radioactive material to break down into its "decay product".

Some radioactive materials have short half-lives; some have long half-lives. Uranium and thorium have long half-lives and so persist in Earth's crust, but radioactive elements with short half-lives have generally disappeared. This suggested that it might be possible to measure the age of Earth by determining the relative proportions of radioactive materials in geological samples. In reality, radioactive elements do not always decay into nonradioactive ("stable") elements directly, instead, decaying into other radioactive elements that have their own half-lives and so on, until they reach a stable element. These "decay chains", such as the uranium-radium and thorium series, were known within a few years of the discovery of radioactivity and provided a basis for constructing techniques of radiometric dating.

The pioneers of radioactivity were chemist Bertram B. Boltwood and physicist Rutherford. Boltwood had conducted studies of radioactive materials as a consultant, and when Rutherford lectured at Yale in 1904, Boltwood was inspired to describe the relationships between elements in various decay series. Late in 1904, Rutherford took the first step toward radiometric dating by suggesting that the alpha particles released by radioactive decay could be trapped in a rocky material as helium atoms. At the time, Rutherford was only guessing at the relationship between alpha particles and helium atoms, but he would prove the connection four years later.

Soddy and Sir William Ramsay had just determined the rate at which radium produces alpha particles, and Rutherford proposed that he could determine the age of a rock sample by measuring its concentration of helium. He dated a rock in his possession to an age of 40 million years by this technique. Rutherford wrote of addressing a meeting of the Royal Institution in 1904:

"I came into the room, which was half dark, and presently spotted Lord Kelvin in the audience and realized that I was in trouble at the last part of my speech dealing with the age of the Earth, where my views conflicted with his. To my relief, Kelvin fell fast asleep, but as I came to the important point, I saw the old bird sit up, open an eye, and cock a baleful glance at me! Then a sudden inspiration came, and I said, "Lord Kelvin had limited the age of the Earth, provided no new source was discovered. That prophetic utterance refers to what we are now considering tonight, radium!" Behold! the old boy beamed upon me."

Rutherford assumed that the rate of decay of radium as determined by Ramsay and Soddy was accurate and that helium did not escape from the sample over time. Rutherford's scheme was inaccurate, but it was a useful first step. Boltwood focused on the end products of decay series. In 1905, he suggested that lead was the final stable product of the decay of radium. It was already known that radium was an intermediate product of the decay of uranium. Rutherford joined in, outlining a decay process in which radium emitted five alpha particles through various intermediate products to end up with lead, and speculated that the radium–lead decay chain could be used to date rock samples. Boltwood did the legwork and by the end of 1905 had provided dates for 26 separate rock samples, ranging from 92 to 570 million years. He did not publish these results, which was fortunate because they were flawed by measurement errors and poor estimates of the half-life of radium. Boltwood refined his work and finally published the results in 1907.

Boltwood's paper pointed out that samples taken from comparable layers of strata had similar lead-to-uranium ratios, and that samples from older layers had a higher proportion of lead, except where there was evidence that lead had leached out of the sample. His studies were flawed by the fact that the decay series of thorium was not understood, which led to incorrect results for samples that contained both uranium and thorium. However, his calculations were far more accurate than any that had been performed to that time. Refinements in the technique would later give ages for Boltwood's 26 samples of 410 million to 2.2 billion years.

Arthur Holmes establishes radiometric dating
Although Boltwood published his paper in a prominent geological journal, the geological community had little interest in radioactivity. Boltwood gave up work on radiometric dating and went on to investigate other decay series. Rutherford remained mildly curious about the issue of the age of Earth but did little work on it.

Robert Strutt tinkered with Rutherford's helium method until 1910 and then ceased. However, Strutt's student Arthur Holmes became interested in radiometric dating and continued to work on it after everyone else had given up. Holmes focused on lead dating because he regarded the helium method as unpromising. He performed measurements on rock samples and concluded in 1911 that the oldest (a sample from Ceylon) was about 1.6 billion years old. These calculations were not particularly trustworthy. For example, he assumed that the samples had contained only uranium and no lead when they were formed.

More important research was published in 1913. It showed that elements generally exist in multiple variants with different masses, or "isotopes". In the 1930s, isotopes would be shown to have nuclei with differing numbers of the neutral particles known as "neutrons". In that same year, other research was published establishing the rules for radioactive decay, allowing more precise identification of decay series.

Many geologists felt these new discoveries made radiometric dating so complicated as to be worthless. Holmes felt that they gave him tools to improve his techniques, and he plodded ahead with his research, publishing before and after the First World War. His work was generally ignored until the 1920s, though in 1917 Joseph Barrell, a professor of geology at Yale, redrew geological history as it was understood at the time to conform to Holmes's findings in radiometric dating. Barrell's research determined that the layers of strata had not all been laid down at the same rate, and so current rates of geological change could not be used to provide accurate timelines of the history of Earth.

Holmes' persistence finally began to pay off in 1921, when the speakers at the yearly meeting of the British Association for the Advancement of Science came to a rough consensus that Earth was a few billion years old and that radiometric dating was credible. Holmes published The Age of the Earth, an Introduction to Geological Ideas in 1927 in which he presented a range of 1.6 to 3.0 billion years. No great push to embrace radiometric dating followed, however, and the die-hards in the geological community stubbornly resisted. They had never cared for attempts by physicists to intrude in their domain, and had successfully ignored them so far. The growing weight of evidence finally tilted the balance in 1931, when the National Research Council of the US National Academy of Sciences decided to resolve the question of the age of Earth by appointing a committee to investigate.

Holmes, being one of the few people who was trained in radiometric dating techniques, was a committee member and in fact wrote most of the final report. Thus, Holmes' report concluded that radioactive dating was the only reliable means of pinning down a geologic time scale. Questions of bias were deflected by the great and exacting detail of the report. It described the methods used, the care with which measurements were made, and their error bars and limitations.

Modern radiometric dating
Radiometric dating continues to be the predominant way scientists date geologic time scales. Techniques for radioactive dating have been tested and fine-tuned on an ongoing basis since the 1960s. Forty or so different dating techniques have been utilized to date, working on a wide variety of materials. Dates for the same sample using these different techniques are in very close agreement on the age of the material. Possible contamination problems do exist, but they have been studied and dealt with by careful investigation, leading to sample preparation procedures being minimized to limit the chance of contamination.

Use of meteorites
An age of 4.55 ± 0.07 billion years, very close to today's accepted age, was determined by Clair Cameron Patterson using uranium–lead isotope dating (specifically lead–lead dating) on several meteorites including the Canyon Diablo meteorite and published in 1956. The quoted age of Earth is derived, in part, from the Canyon Diablo meteorite for several important reasons and is built upon a modern understanding of cosmochemistry built up over decades of research. Most geological samples from Earth are unable to give a direct date of the formation of Earth from the solar nebula because Earth has undergone differentiation into the core, mantle, and crust, and this has then undergone a long history of mixing and unmixing of these sample reservoirs by plate tectonics, weathering and hydrothermal circulation.

All of these processes may adversely affect isotopic dating mechanisms because the sample cannot always be assumed to have remained as a closed system, by which it is meant that either the parent or daughter nuclide (a species of atom characterised by the number of neutrons and protons an atom contains) or an intermediate daughter nuclide may have been partially removed from the sample, which will skew the resulting isotopic date. To mitigate this effect it is usual to date several minerals in the same sample, to provide an isochron. Alternatively, more than one dating system may be used on a sample to check the date.

Some meteorites are furthermore considered to represent the primitive material from which the accreting solar disk was formed. Some have behaved as closed systems (for some isotopic systems) soon after the solar disk and the planets formed. To date, these assumptions are supported by much scientific observation and repeated isotopic dates, and it is certainly a more robust hypothesis than that which assumes a terrestrial rock has retained its original composition.

Nevertheless, ancient Archaean lead ores of galena have been used to date the formation of Earth as these represent the earliest formed lead-only minerals on the planet and record the earliest homogeneous lead–lead isotope systems on the planet. These have returned age dates of 4.54 billion years with a precision of as little as 1% margin for error.

Statistics for several meteorites that have undergone isochron dating are as follows:

Canyon Diablo meteorite

The Canyon Diablo meteorite was used because it is both large and representative of a particularly rare type of meteorite that contains sulfide minerals (particularly troilite, FeS), metallic nickel-iron alloys, plus silicate minerals. This is important because the presence of the three mineral phases allows investigation of isotopic dates using samples that provide a great separation in concentrations between parent and daughter nuclides. This is particularly true of uranium and lead. Lead is strongly chalcophilic and is found in the sulfide at a much greater concentration than in the silicate, versus uranium. Because of this segregation in the parent and daughter nuclides during the formation of the meteorite, this allowed a much more precise date of the formation of the solar disk and hence the planets than ever before.

The age determined from the Canyon Diablo meteorite has been confirmed by hundreds of other age determinations, from both terrestrial samples and other meteorites. The meteorite samples, however, show a spread from 4.53 to 4.58 billion years ago. This is interpreted as the duration of formation of the solar nebula and its collapse into the solar disk to form the Sun and the planets. This 50 million year time span allows for accretion of the planets from the original solar dust and meteorites.

The Moon, as another extraterrestrial body that has not undergone plate tectonics and that has no atmosphere, provides quite precise age dates from the samples returned from the Apollo missions. Rocks returned from the Moon have been dated at a maximum of 4.51 billion years old. Martian meteorites that have landed upon Earth have also been dated to around 4.5 billion years old by lead–lead dating. Lunar samples, since they have not been disturbed by weathering, plate tectonics or material moved by organisms, can also provide dating by direct electron microscope examination of cosmic ray tracks. The accumulation of dislocations generated by high energy cosmic ray particle impacts provides another confirmation of the isotopic dates. Cosmic ray dating is only useful on material that has not been melted, since melting erases the crystalline structure of the material, and wipes away the tracks left by the particles.

Altogether, the concordance of age dates of both the earliest terrestrial lead reservoirs and all other reservoirs within the Solar System found to date are used to support the fact that Earth and the rest of the Solar System formed at around 4.53 to 4.58 billion years ago.

title: Age of Earth