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Talk:Compact space

Is "hyperreal definition" specific to metric spaces?
I'm concerned that the "Hyperreal definition" subsubsection is not stated as being specific to metric spaces. It's not clear to me what being "infinitely close to a point of X" might mean, if there is no metric around. Should this section be merged into the "Metric spaces" section? What about the paragraph just above it, the second paragraph of "Characterization by continuous functions", which by the way also seems to be redundant with "Hyperreal definition"? --Trovatore (talk) 07:02, 12 July 2018 (UTC)

The most standard definition is not prominent enough
I think it is not too bold to say that the nearly universal agreement among mathematicians is that the word "compact" by itself, in the most general context and without further qualification, means that every open cover has a finite subcover. I am not saying that definition should appear in the first sentence; we've discussed this before and I agree with opening more gently with the example of closed and bounded subsets of a Euclidean space.

But I am saying that the third sentence of the six-sentence fourth paragraph is way too deeply buried.

I know that Sławomir has strong feelings about the importance of sequential compactness, and that's fine; I don't care to argue that point. Just the same, when the distinction is made explicitly, sequential compactness is the one that takes the adjective; compactness simpliciter is the cover definition. This is entirely standard in the literature.

I don't have an immediate proposal but I do think the standard general definition needs to be treated earlier and more prominently. --Trovatore (talk) 07:17, 12 July 2018 (UTC)

Heine-Cantor?
The introduction to the Definitions section mentions "Dirichlet's theorem". It seems to me that this is actually meant to refer to the Heine–Cantor theorem, but I don't feel competent enough to edit the article. — Preceding unsigned comment added by 2A02:8070:A191:7D00:AB:87BA:3A49:1844 (talk) 12:23, 20 January 2019 (UTC)

What does it mean?!
I think this part is wrong or vague:

"typical examples of compact spaces include spaces consisting not of geometrical points but of functions."

Mojtabakd (talk) 09:22, 8 November 2019 (UTC)
 * I agree, and I have completely rewritten the paragraph. D.Lazard (talk) 10:13, 8 November 2019 (UTC)

"Since a continuous image of a compact space is compact, the extreme value theorem"
That is not grammatical English, at the very least, a verb must be adduced, e.g. the extreme value theorem follows, or since... we have... etc. 2A01:CB0C:CD:D800:C12E:287B:1E8A:E532 (talk) 20:44, 1 February 2021 (UTC)

`Subsequence' in this article is different from the linked subsequence
The introduction states:
 * One such generalization is that a topological space is sequentially compact if every infinite sequence of points sampled from the space has an infinite subsequence that converges to some point of the space.

While this is true for subsequences $$(s_{i_n})_n$$ of $$(s_n)_n$$ with $$\forall n, i_n < i_{n+1}$$, the article subsequence specifically states that subsequences are defined in terms of $$\leq$$ instead of $${<}$$:
 * Subsequences can contain consecutive elements which were not consecutive in the original sequence.

That does not make sense here, since it would allow one to prove that every subset of a metric space is compact via the constant "subsequence" (or, equivalently, every topological space is sequentially compact). The non-strict comparison is also in contrast to the linked reference that explicitely defines the index sequence via $${<}$$ as well as, for example,. In my opinion, it should be made clear - either here or in subsequence - that (non-)strictness matters depending on the context. --217.251.39.96 (talk) 23:23, 9 May 2021 (UTC)
 * Apparently you confuse "consecutive" and "equal", or you confuse elements of the sequence with their indexes. Said otherwise, the definition of "subsequence" implies $$\forall n, i_{n+1} > i_n,$$ and your second quotation means that one may have $$i_{n +1} > 1+ i_{n}.$$ For example, the positive even integers form a subsequence of the positive integers; the integers 6 and 8 are consecutive in the subsequence of even integers, but not in the integers, since 7 is between them. D.Lazard (talk) 08:49, 10 May 2021 (UTC)

Pavel Urysohn
The article mentions a notion introduced by Alexandrov and Urysohn in 1929. However Urysohn drowned in 1923. The works attributed to both at later dates is due to Alexandrov.

Not a universal property
In the modification by he refers to the following characterisation of a compact space : "$X$ is compact if and only if for every topological space $Y$, the projection $X \times Y \to Y$ is a closed mapping" as a universal property. This is not the case : a universal property is a categorical construction, not the definition of a class of objects in a category. A compactification of a topological space is defined by a universal property but the notion of a compact space is not. Unless this is satisfactorily explained by Taku I'm going to revert this again.

I also see no reason to separate this characterisation from the others: of course it is distinct from the others, otherwise there'd be no reason to have it on the list. Either change the presentation to have a series of paragraphs for each characterisation, perhaps grouping those which are most similar to each other as the various ones using filters or limit points, or have a list for all characterisation without singling out one over the others. jraimbau (talk) 14:13, 13 September 2022 (UTC)

 * Of course, a construction in category theory can be characterized by a universal property but we can also talk about a universal property of non-construction. So, I think it’s a matter of how one uses the term "universal property" (only for constructions or more generally). Anyway, the reference (Bourbaki) doesn’t use the term "universal property" so I can agree to avoid the term, since you think it’s a wrong usage.

 * As for separating it from the list: another reason I didn’t add it to the list was that this characterization is not a definition of a compact space, as far as I can tell. On the other than, some others like filter ones are one of the definition of a compact space; for example, Bourbaki defines a compact (or rather a quasi-compact space) in terms of a filter. We shouldn’t give a misleading impression that the projection characterization is a definition of a compact space.
 * Oh and one more reason: one of a definition of a proper map is that it is a universally closed map. So, a compact space is an absolute version of a proper map or the latter is a relative version of the former. That type of discussion will be awkward to do in the list. -- Taku (talk) 15:44, 13 September 2022 (UTC)
 * Regarding universal property : there is a proper definition for what this is (of which most people studying "pure" mathematics have an intuition through various examples), so i strongly think that informal usage of the term should be avoided when discussing math formally.
 * I don't like the list format much here either but if it is used i think it should be used consistently. If one of the characterisations is of particular interest and you want to have a more detailed discussion of it i think you'd be better off putting it in a separate subsection. In fact, the list given here seems flawed in terms of presentation : a few paragraphs above it the usual general definition of compacity (open covers) is given, and it is repeated as item #2 in the list. Maybe a better way to present it would be to split it into several subsections each giving an alternate definition (maybe called "characterisation" if it does not feel like a definition, as seems to be the case with #12). Looking briefly at the list it seems that #2-3 and #6-11 should be grouped together (and so #3 put in the "open cover definition") ; #6-11 could be put in a section called "sequential definition and generalisations" ; that leaves #4, 5 and 12 which could each have their own subsection if puffed up, or for the moment just put into a section called "alternate characterisations" or something else to this effect, avoiding the list format. jraimbau (talk) 15:35, 14 September 2022 (UTC)

Each subset is closed if and only if it is compact
In a compact Hausdorff space, each closed subset is compact and each compact subset is closed. (Here, "subset" means proper or improper.) Is there an example of a compact non-Hausdorff space where each subset is closed if and only if it is compact? If so, let's add it to the article. — Q uantling (talk | contribs) 19:08, 1 June 2023 (UTC)

Strange use of "collection" and "subcollection"
This article uses collection and subcollection many times, in contradistinction to "set", "subset", "class" or "subclass". I'm not sure why... collection is an informal term (more a part of the language of naive set theory than topology) and it's appearance here is strange. Is this an attempt to make the article more readable? Ross Fraser (talk) 00:49, 24 August 2023 (UTC)

 * It's used when there are "sets of sets"; instead one says "collections of sets" even though there is no change in meaning. That way when one says, let $A$ be a collection or let $A$ be a set, one knows instantly whether $A$ is one of the containing sets or one of the contained sets.  I guess that means that it is for readability.
 * In contrast "class" is not synonymous with "set", so it would be a poor choice in the present article. — Q uantling (talk | contribs) 01:29, 24 August 2023 (UTC)
 * I see at the Family of sets article that "family" (and "subfamily") could be used instead of "collection" (and "subcollection") in this compact space article. I prefer the latter because it is what I was taught, but if you feel strongly then you could change it to the former and I would live with that. — Q uantling (talk | contribs) 13:31, 24 August 2023 (UTC)
 * Full disclosure: I have just edited the Family of sets article, so that article no longer is an independent voice in this discussion. — Q uantling (talk | contribs) 16:02, 24 August 2023 (UTC)

"every non-Hausdorff TVS contains compact (and thus complete) subsets that are not closed"
This doesn't seem to be correct. In the cocountable topology, the only compact sets are the finite sets. These are closed, as the cocountable topology is T1. But the cocountable topology on an uncountable set is not Hausdorff. 2A02:A03F:8CEC:D00:CC18:E805:F3B7:DD52 (talk) 16:56, 3 January 2024 (UTC)

 * Good observation, but I think the cocountable topology is not a TVS topology because addition is not continuous (any T1 topological group is hausdorff). A reference would be nice though. Tito Omburo (talk) 17:38, 3 January 2024 (UTC)

 * After further reflection, the singleton $$\{0\}$$ is compact, and is closed iff the topology is hausdorff. Tito Omburo (talk) 17:47, 3 January 2024 (UTC)

Proof for equivalent condition 12 in "Characterizations"
Link: https://imgur.com/a/y59lw01

Note: this proof depends on the axiom of choice (AC). Without it, I am not sure it is possible to prove that condition 12 is equivalent to compactness.

Now, is it possible to prove AC from the equivalence of compactness to condition 12? I don't know.

If so, it may be related to the collection of partial well orderings of a set X. A couple of observations:

 * 1) the collection of partial well orderings of a set X is partially ordered by initial segment relation, x <= x' if x is an initial segment of x'
 * 2) it may be possible to endow this partially ordered set with a topology and thereby obtain a link between AC, the well ordering theorem, and equivalence of compactness to condition 12

Cheers,

24.43.142.162 (talk) 04:07, 25 March 2024 (UTC)

 * Hi 24.43.142.162, and thanks for your contribution.
 * Could you provide an external reference for the proposition you added to the article? E.g, a book where the proof (or at least the statement) can be found? Otherwise, per Wikipedia's policies, it will be considered "original research" (the term has a special meaning on Wikipedia, see WP:OR) and will eventually be removed.
 * Note that it does not matter that you provided a proof: the core principle of Wikipedia is that it is not an authoritative source, but a well-structured synthesis that provides links to external sources (also note that since contributors are anonymous and anybody can contribute, you can't trust contributors to check the logic behind scientific arguments). So, even though that might be annoying to you, your proof is worthless in that context. If you want to contribute proofs to a collaborative encyclopedia, you can check ProofWiki.
 * Cheers, Malparti (talk) 13:37, 25 March 2024 (UTC)

 * Fine, then remove it, write a letter to American Mathematical Monthly with the proof included, tell them that you've submitted my proof, in care of yourself, and the publication should bear that authorship (by X (me) in care of you). When they publish it, you can add this proof back and cite the publication, year, month, issue, page, etc...
 * If you get started quick you might have it done by the end of the year!

 * 24.43.142.162 (talk) 14:51, 25 March 2024 (UTC)

title: Talk:Compact space


text:
Fairchild Channel F

The Fairchild Channel F, short for "Channel Fun", is a video game console, the first to be based on a microprocessor and to use ROM cartridges (branded 'Videocarts') instead of having games built-in. It was released by Fairchild Camera and Instrument in November 1976 across North America at a retail price of US$169.95 1976. It was launched as the "Video Entertainment System", but when Atari released its Video Computer System (VCS) the next year, Fairchild rebranded their console as "Channel F" while keeping the Video Entertainment System descriptor.

The Fairchild Channel F achieved only about 350,000 units before Fairchild sold the technology to Zircon International in 1979, trailing well behind the VCS. The system was discontinued in 1983.

History
In 1974, Alpex Computer Corporation employees Wallace Kirschner and Lawrence Haskel developed a home video game prototype consisting of a base unit centered on an Intel 8080 microprocessor and interchangeable circuit boards containing ROM chips that could be plugged into the base unit. The duo attempted to interest several television manufacturers in the system, but were unsuccessful. Next, they contacted a buyer at Fairchild, which sent engineer Jerry Lawson to evaluate the system. Lawson was impressed by the system and suggested Fairchild license the technology, which the company did in January 1976.

Lawson worked with industrial designer Nick Talesfore and mechanical engineer Ron Smith to turn the prototype into a viable project. Jerry Lawson replaced the 8080 with Fairchild's own F8 CPU; while Nick Talesfore and Ron Smith were responsible for adapting the prototype's complex keyboard controls into a single control stick, and encasing the ROM circuit boards into plastic cartridges reminiscent of 8-track tapes. Talesfore, providing Industrial Design (ID), and Ron Smith, providing Mechanical Engineering (ME), collaborated on the styling and function of the 8 degrees of freedom hand controller. They were responsible for the design of the hand controllers, console, and video game cartridges. In addition to providing the ID for this system, Talesfore also art directed Tom Kamafugi, the graphic designer who did the original graphic design for the early video cartridges cartons.

The system was also released in Japan (チャンネル F ) in October 1977.

Channel F System II

Lawson moved on to form his own company, Video Soft in 1980. Talesfore continued working on the system at Fairchild, and eventually a number of these improvements resulted in the improved System II. The major changes were that the controllers were now removable, using the Atari joystick port connector (not Atari compatible), and their storage was moved to the back of the machine. The sound was now mixed into the RF modulator so you could adjust it on your TV set instead of a fixed volume internal speaker. The internal electronics were also simplified, with two custom logic chips replacing the standard TTL logic chips. This resulted in a much smaller motherboard which allowed for a smaller, simpler and more modern-looking case design.

Some time in 1979, Zircon International bought the rights to the Channel F and released the re-designed console as the Channel F System II to compete with Atari's VCS. Channel F II struggled, managing to only release six new games after the debut before its demise; several of these were developed at Fairchild before they sold the rights.

Licensed variants
A number of licensed versions were released in Europe, including the Luxor Video Entertainment System in Sweden, Adman Grandstand Video Entertainment Computer (Channel F II) in the UK, the SABA Videoplay, ITT Telematch Processor and Nordmende Color TelePlay μP from Germany, and the Barco Challenger, Dumont Videoplay and Emerson Videoplay from the Barco/Dumont/Emerson company in Italy and Belgium. Swedish Luxor also released the Channel F II as Luxor Video Entertainment Computer.

Design

The F8 was very innovative compared to the existing processors and typical integrated circuits of the day. Because chip packaging was not initially available with enough pins, a few pins were used to communicate with other chips in the system. You needed at least two chips to set up an F8 processor system to be able run any code. The savings from using standard pin layout enabled the inclusion of 64 Bytes of internal scratchpad RAM in the CPU. The VES/Channel F, as well as the System II, had one CPU and two storage chips (PSU:s). (A single-chip variant of the F8 was used by the VideoBrain computer system).

The Channel F is able to use one plane of graphics and one of four background colors per line, with three plot colors to choose from (red, green, and blue) that turns white if the background is set to black, at a resolution of 128 × 64, with approximately 104 × 60 pixels visible on the TV screen. This VRAM or framebuffer was "write only" and not usable for anything else. There was only 64 Bytes of scratchpad RAM for general use - half the amount of the later Atari 2600. The Maze game (Videocart-10) and Hangman game (Videocart-18) used 1024 bits of on-cartridge static RAM connected directly to one PSU port - adding to the cost of manufacturing it. The Chess game contained considerably more on-cartridge RAM than that, 2048 Bytes accomplished by using an F8 memory interface circuit to be able to use industry standard ROM and RAM. The F8 processor at the heart of the console is able to produce enough AI to allow for player versus computer matches, a first in console history. All previous machines required a human opponent. Tic-Tac-Toe on Videocart-1 had this feature, it was only for one player against the machine. The same is true for the chess game, which could have very long turn times for the computer as the game progressed, depending on the set difficulty.

In the original unit, sound is played through an internal speaker, rather than the TV set. However, the System II passed sound to the television through the RF modulator.

The Channel F is also the first video game console to feature a pause function; There is a 'Hold' button on the main unit of the console which allows players to freeze inside the two built-in games and change several game settings in the meantime. Button is controlled through code so it was used for other things in other games.

Controllers
The controllers are a joystick without a base; the main body is a large handgrip with a triangular "cap" on top, the top being the portion that actually moved for eight-way directional control. It could be used as both a joystick and paddle (twist), and not only could it be pushed down to operate as a fire button, it could be pulled up as well. The model 1 unit contained a small compartment for storing the controllers when moving it or when not in use. The System II featured detachable controllers with two holders at the back to wind the cable around and to store the controller in. Zircon later offered a special controller that featured an action button on the front of the joystick. It was marketed by Zircon as "Channel F Jet-Stick" in a letter sent out to registered owners before Christmas 1982.

One feature, unique to the console, is the 'hold' button, which allows the player to freeze the game, change the time or speed of the game. The hold function is however not universal (like the hardwired reset) as the four buttons are set up in code. The programmer can choose their function/purpose. The text labels explains the button functions in the built-in games (and some of the Videocarts).

Despite the failure of the Channel F, the joystick's design was so popular—Creative Computing called it "outstanding"— that Zircon also released an Atari joystick port-compatible version, the Video Command Joystick, first released without the extra fire button. Before that, only the downwards plunge motion was connected and acted as the fire button; the pull-up and twist actions were not connected to anything.

Technical specifications

 * CPU microprocessor: Fairchild F8 (8-bit) operating at 1.7897725 MHz (NTSC colorburst/2). PAL gen. 1: 2.0000 MHz, gen. 2: 1.9704910 MHz (double PAL colorburst/9)
 * RAM: 2 KB VRAM (128 × 64 × 2 bits) for the write only framebuffer (four Mostek MK4027 or MK4015 4Kx1bit DRAMs), plus 64 bytes of scratchpad memory.
 * Additional SRAM supported via add-in cartridges. Maze and Hangman has 1K x 1 bit, expanded with 3853 SMI Chess has 2048 Bytes.
 * Resolution: Approximately columns 3-107 and rows 2-62 are visible, depending on TV. (Columns 125 and 126 controls palette per row). Although VRAM could cover 128 × 64 pixels,
 * Refresh rate: 60 Hz
 * Colors: 8 colors (either black/white lines or lines using background grey/blue/green with red, green or blue pixels)
 * Audio: 120 Hz, 500 Hz and 1 kHz beeps (can be modulated to produce different tones). Quality is quite superior on the System II, versus the original model.
 * Input: two custom game controllers, hardwired to the console (original release) or removable (Channel F System II)
 * Output: RF modulated composite video signal, cord hardwired to console in original release, detachable in System II.

Games
Twenty-seven cartridges, termed "Videocarts", were officially released to consumers in the United States during the ownership of Fairchild and Zircon, the first twenty-one of which were released by Fairchild. Several of these cartridges were capable of playing more than one game and were typically priced at. The Videocarts were yellow and approximately the size and overall texture of an 8 track cartridge. They usually featured colorful label artwork. The earlier artwork was created by nationally known artist Tom Kamifuji and art directed by Nick Talesfore. The console contained two built-in games, Tennis and Hockey, which were both advanced Pong clones. In Hockey, the reflecting bar could be changed to different diagonals by twisting the controller knob and could move all over the playing field. Tennis was much like the original Pong.

A sales brochure from 1978 listed "Keyboard Videocarts" for sale. The three shown were K-1 Casino Poker, K-2 Space Odyssey, and K-3 Pro-Football. These were intended to use the Keyboard accessory, which is displayed on the Channel F II box. All further brochures, released after Zircon took over from Fairchild, never listed this accessory nor anything called a Keyboard Videocart.

There was one cartridge released outside the numbered series, listed as Videocart-51 and simply titled "Demo 1". This Videocart was shown in a single sales brochure released shortly after Zircon acquired the company. It has not been seen listed for sale after this single brochure which was sent out in the winter of 1979.

 * Democart (was briefly available to the general public)
 * Democart 2

Unreleased carts:
 * Keyboard Videocart-1: Casino Poker
 * Keyboard Videocart-2: Space Odyssey
 * Keyboard Videocart-3: Pro-Football

German electronics manufacturer SABA also released a few compatible carts different from the original carts: translation in Videocart-1 Tic-Tac-Toe to German words, Videocart-3 released with different abbreviations (German), and Videocart-18 changed graphics and has a German word list.

In 2021, a number of new 'Homebrew' games were released on itch.io by retro developer Arlasoft. These included ports of mobile puzzle games Tents & Trees, 2048 and Threes, as well as a port of the classic arcade shooter Centipede. Through a secret button combination a hidden game could also be started, the box and instruction booklet has multiple hints about the needed code. These were released on cartridge as Videocart-29.

Reception
The Channel F had beaten the Atari VCS to the market, but once the VCS was released, sales of the Channel F fell, attributed to the types of games that were offered. Most of the Channel F titles were slow-paced educational and intellectual games, compared to the action-driven games that launched with the VCS. Even with the redesigned Channel F II in 1978, Fairchild was unable to meet the sales that the VCS and its games were generating. By the time Fairchild sold the technology to Zircon in 1979, around 350,000 total units had been sold.

Ken Uston reviewed 32 games in his book Ken Uston's Guide to Buying and Beating the Home Video Games in 1982, and rated some of the Channel F's titles highly; of these, Alien Invasion and Video Whizball were considered by Uston to be "the finest adult cartridges currently available for the Fairchild Channel F System". The games on a whole, however, rated last on his survey of over 200 games for the Atari, Intellivision, Astrocade and Odyssey consoles, and contemporary games were rated "Average" with future Channel F games rated "below average". Uston rated almost one-half of the Channel F games as "high in interest" and called that "an impressive proportion" and further noted that "Some of the Channel F cartridges are timeless; no matter what technological developments occur, they will continue to be of interest." His overall conclusion was that the games "serve a limited, but useful, purpose" and that the "strength of the Channel F offering is in its excellent educational line for children".

In 1983, after Zircon announced its discontinuation of the Channel F, Video Games reviewed the console. Calling it "the system nobody knows", the magazine described its graphics and sounds as "somewhat primitive by today's standards". It described Space War as "may be the most antiquated game of its type still on the market", and rated the 25 games for the console with an average "interest grade" of three ("not too good") on a scale from one to ten and "skill rating" at an average 4,5 of 10. The magazine stated, however, that Fairchild "managed to create some fascinating games, even by today's standards", calling the poker game Casino Royale (actually Videocart-25, Casino Poker) "the best card game, from blackjack to bridge, made for any TV-game system". It also favorably reviewed Dodge-It ("simple but great"), Robot War ("Berzerk without guns"), and Whizball ("thoroughly original ... hockey with guns"), but concluded that only those interested in nostalgia, video game collecting, or card games would purchase the Channel F in 1983.

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

title: Fairchild Channel F


text:
Talk:Company (disambiguation)

Comments
I disagree with many of the statements in Company, but rather than change them on my own say so, felt that discussion was more appropriate.

> A company (or corporation) is a legal? entity chartered by the state for a particular purpose.

What do we mean by "chartered"? Some historical companies have been formally chartered by the state, but others are simply licensed or recognized, allowing them to do business. Yet other companies, private partnerships or sole owner companies, simply file public notice concerning a fictitious business name and go into business without needing formal recognition from the state.

> Sometimes called a "fictional person" a company enjoys many of the rights? and responsibilities? of individual citizens? such as the ability to own property, sign binding contracts?, pay taxes?, and otherwise participate in society?.

To my knowledge this applies only to formal corporations (by whatever name applies in the nationality involved). Non-corporate companies do not have these rights and abilities, but instead the owners of the company individually and/or jointly own property, sign contracts, etc.

> American corporations are typically chartered in Delaware?.

No, American corporations are typically chartered in the state where the founding members live or do business. Every state has large numbers of corporations, and I expect there are fewer in Delaware than in many of the larger states.

Some states do have specific laws which grant more protections to corporations, either in general or to specific types of corporations. Because of this, financial corporations (such as credit card companies) often choose to incorporate in Delaware. However, other types of corporations will likewise choose to incorporate in other states which are friendly to their type of company. -- In my experience, "company" is primarily used to refer to corporations. I suppose it can be used to refer to a partnership, although I at least would not normally call partnerships companies. I cannot see how you can call a single proprietorship a company though -- the fundamental meaning of company is a group of individuals -- how can a single person be a group?

Not all corporations are companies though. Many government agencies or non-profit organizations are called "corporations", but I wouldn't call them companies. And I don't think you could call a corporation sole a company, based on the definition of "company".

All corporations have to be chartered in some sense. Historically, there are three different ways in English law a company can be established: by royal charter, by special act of Parliament passed to create that particular company, or by registration under a general Corporations Act. Often, only companies established by royal charter or act of Parliament are referred to as having a "charter" (although maybe usage is different in the US).

Also, I think the US is somewhat unusual in having different corporations laws in each state. Most countries (e.g. Australia) have a national corporations law. There is even some transnational corporations law in development (via the European Company Statute). -- SJK

I think that we are hitting a difference in US English versus UK English. US English company refers to any business, while UK English company refers exclusively to corporations. Maybe move this article over to corporation -- Chenyu

Yes, we might have a problem with language.

"Company" is used to refer to businesses comprised of multiple people. These can be huge multi-national corporations, partnerships, or even single proprieterships and single-owner corporations. The important distinction is that a company has multiple people in the company, owner, clerks, staff, etc. So a company can have a single owner but employ hundreds of people.

As for "charter", I believe that word isn't used much in the USA. A company is founded, or licensed, or incorporated (depending on the type of company).

As for the states, the USA is a union of quasi-national states, a federation of states. Each state has its own business regulations, and the federal government has jurisdiction only over those activities which cross state borders (inter-state commerce).

For-profit entity or non profit entity acting as the General Partner
A friend and I are about to form a partnership including a for-profit entity, and a non-profit entity among the partners. We are attempting to determine whether the for-profit entity should be one of the General Partners or one of the limited partners. Or is it better for the non-profit to be the General Partners, and not one of the limited partners. What are the tax and operating benefits in each case?

Disambiguating this page
I a disambiguating this page, and just so everyone know's what I'm doing, here's my criteria for how I am determining what to link to:
 * 1) If it's clearly a corporation I am linking to corporation.
 * 2) If the text is ambiguous about what type of company it is I am linking to types of companies.
 * 3) If the article is using the generic meaning of company (eg. Some companies do business in many countries.) then I will link to types of companies.

Kevin Rector 13:41, Jul 23, 2004 (UTC)

 * I have changed the redirect for "Company" back to "Company (law)" and put a link to the disambiguation page at the top of "Company (law)". That is how it was previously and I think that is the sensible approach.  Wikipedia doesn't keep stats, but it seems to me highly likely that 99% of the hits for company will be for the legal entity as opposed to the military term or a number of obscure films or books.  Happy to hear other points of view, but that seems to me to be the most sensible approach. I appreciate that Americans and Canadians refer to companies as corporations, but I still think that if you just aggregate the Brits, the Ozzies, the Kiwis and other Commonwealth countries, the business entity is going to be by far the bulk of the hits as opposed to the other options on the disambiguation page. Legis 08:43, 16 June 2006 (UTC)

Other obscure uses of company
"The company" was also used by Joseph Conrad in the Heart of Darkness to refer to the greed of European colonisers in Africa. Starfish9 23:36, 15 July 2006 (UTC)

DABs are not collections of vaguely related articles
A disambiguation page is not a thesaurus entry, with pointers to articles that might be vaguely related to the term in question. It is essentially a list of articles that could conceivably have that term as their title, if Wikipedia didn't require unique titles. Accordingly, I have deleted all the vaguely related items, such as interpersonal relationship and concubine. Additionally, if there is a primary term, as is the case with company, it should be in the first line, before the list of subsidiary entries—I have fixed this as well. I've made some other minor changes to bring this page more in line with the Guidelines and Manual of Style. These both provide a great explanation of the purpose of disambiguation pages—anyone editing a DAB should read them. —johndburger 00:52, 27 October 2010 (UTC)

I wann all pets and rare Things in adopt me pls trank you
Huge fan! My user name of roblox:Alpetannelanne820 2A02:8108:8080:3534:3CD3:546B:317D:CFBA (talk) 12:10, 31 May 2024 (UTC)

title: Talk:Company (disambiguation)


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Collation

Collation is the assembly of written information into a standard order. Many systems of collation are based on numerical order or alphabetical order, or extensions and combinations thereof. Collation is a fundamental element of most office filing systems, library catalogs, and reference books.

Collation differs from classification in that the classes themselves are not necessarily ordered. However, even if the order of the classes is irrelevant, the identifiers of the classes may be members of an ordered set, allowing a sorting algorithm to arrange the items by class.

Formally speaking, a collation method typically defines a total order on a set of possible identifiers, called sort keys, which consequently produces a total preorder on the set of items of information (items with the same identifier are not placed in any defined order).

A collation algorithm such as the Unicode collation algorithm defines an order through the process of comparing two given character strings and deciding which should come before the other. When an order has been defined in this way, a sorting algorithm can be used to put a list of any number of items into that order.

The main advantage of collation is that it makes it fast and easy for a user to find an element in the list, or to confirm that it is absent from the list. In automatic systems this can be done using a binary search algorithm or interpolation search; manual searching may be performed using a roughly similar procedure, though this will often be done unconsciously. Other advantages are that one can easily find the first or last elements on the list (most likely to be useful in the case of numerically sorted data), or elements in a given range (useful again in the case of numerical data, and also with alphabetically ordered data when one may be sure of only the first few letters of the sought item or items).

Numerical and chronological
Strings representing numbers may be sorted based on the values of the numbers that they represent. For example, "−4", "2.5", "10", "89", "30,000". Pure application of this method may provide only a partial ordering on the strings, since different strings can represent the same number (as with "2" and "2.0" or, when scientific notation is used, "2e3" and "2000").

A similar approach may be taken with strings representing dates or other items that can be ordered chronologically or in some other natural fashion.

Alphabetical
Alphabetical order is the basis for many systems of collation where items of information are identified by strings consisting principally of letters from an alphabet. The ordering of the strings relies on the existence of a standard ordering for the letters of the alphabet in question. (The system is not limited to alphabets in the strict technical sense; languages that use a syllabary or abugida, for example Cherokee, can use the same ordering principle provided there is a set ordering for the symbols used.)

To decide which of two strings comes first in alphabetical order, initially their first letters are compared. The string whose first letter appears earlier in the alphabet comes first in alphabetical order. If the first letters are the same, then the second letters are compared, and so on, until the order is decided. (If one string runs out of letters to compare, then it is deemed to come first; for example, "cart" comes before "carthorse".) The result of arranging a set of strings in alphabetical order is that words with the same first letter are grouped together, and within such a group words with the same first two letters are grouped together, and so on.

Capital letters are typically treated as equivalent to their corresponding lowercase letters. (For alternative treatments in computerized systems, see Automated collation, below.)

Certain limitations, complications, and special conventions may apply when alphabetical order is used:
 * When strings contain spaces or other word dividers, the decision must be taken whether to ignore these dividers or to treat them as symbols preceding all other letters of the alphabet. For example, if the first approach is taken then "car park" will come after "carbon" and "carp" (as it would if it were written "carpark"), whereas in the second approach "car park" will come before those two words. The first rule is used in many (but not all) dictionaries, the second in telephone directories (so that Wilson, Jim K appears with other people named Wilson, Jim and not after Wilson, Jimbo).
 * Abbreviations may be treated as if they were spelt out in full. For example, names containing "St." (short for the English word Saint) are often ordered as if they were written out as "Saint". There is also a traditional convention in English that surnames beginning Mc and M' are listed as if those prefixes were written Mac.
 * Strings that represent personal names will often be listed by alphabetical order of surname, even if the given name comes first. For example, Juan Hernandes and Brian O'Leary should be sorted as "Hernandes, Juan" and "O'Leary, Brian" even if they are not written this way.
 * Very common initial words, such as The in English, are often ignored for sorting purposes. So The Shining would be sorted as just "Shining" or "Shining, The".
 * When some of the strings contain numerals (or other non-letter characters), various approaches are possible. Sometimes such characters are treated as if they came before or after all the letters of the alphabet. Another method is for numbers to be sorted alphabetically as they would be spelled: for example 1776 would be sorted as if spelled out "seventeen seventy-six", and 24 heures du Mans as if spelled "vingt-quatre..." (French for "twenty-four"). When numerals or other symbols are used as special graphical forms of letters, as in 1337 for leet or Se7en for the movie title Seven, they may be sorted as if they were those letters.
 * Languages have different conventions for treating modified letters and certain letter combinations. For example, in Spanish the letter ñ is treated as a basic letter following n, and the digraphs ch and ll were formerly (until 1994) treated as basic letters following c and l, although they are now alphabetized as two-letter combinations. A list of such conventions for various languages can be found at.

In several languages the rules have changed over time, and so older dictionaries may use a different order than modern ones. Furthermore, collation may depend on use. For example, German dictionaries and telephone directories use different approaches.

Root sorting
Some Arabic dictionaries, such as Hans Wehr's bilingual A Dictionary of Modern Written Arabic, group and sort Arabic words by semitic root. For example, the words kitāba (كتابة 'writing'), kitāb (كتاب 'book'), kātib (كاتب 'writer'), maktaba (مكتبة 'library'), maktab (مكتب 'office'), maktūb (مكتوب 'fate,' or 'written'), are agglomerated under the triliteral root k-t-b (ك ت ب), which denotes 'writing'.

Radical-and-stroke sorting

 * See also Chinese characters and Chinese character orders

Another form of collation is radical-and-stroke sorting, used for non-alphabetic writing systems such as the hanzi of Chinese and the kanji of Japanese, whose thousands of symbols defy ordering by convention. In this system, common components of characters are identified; these are called radicals in Chinese and logographic systems derived from Chinese. Characters are then grouped by their primary radical, then ordered by number of pen strokes within radicals. When there is no obvious radical or more than one radical, convention governs which is used for collation. For example, the Chinese character 妈 (meaning "mother") is sorted as a six-stroke character under the three-stroke primary radical 女.

The radical-and-stroke system is cumbersome compared to an alphabetical system in which there are a few characters, all unambiguous. The choice of which components of a logograph comprise separate radicals and which radical is primary is not clear-cut. As a result, logographic languages often supplement radical-and-stroke ordering with alphabetic sorting of a phonetic conversion of the logographs. For example, the kanji word Tōkyō (東京) can be sorted as if it were spelled out in the Japanese characters of the hiragana syllabary as "to-u-ki-yo-u" (とうきょう), using the conventional sorting order for these characters.

In addition, Chinese characters can also be sorted by stroke-based sorting. In Greater China, surname stroke ordering is a convention in some official documents where people's names are listed without hierarchy.

Automation
When information is stored in digital systems, collation may become an automated process. It is then necessary to implement an appropriate collation algorithm that allows the information to be sorted in a satisfactory manner for the application in question. Often the aim will be to achieve an alphabetical or numerical ordering that follows the standard criteria as described in the preceding sections. However, not all of these criteria are easy to automate.

The simplest kind of automated collation is based on the numerical codes of the symbols in a character set, such as ASCII coding (or any of its supersets such as Unicode), with the symbols being ordered in increasing numerical order of their codes, and this ordering being extended to strings in accordance with the basic principles of alphabetical ordering (mathematically speaking, lexicographical ordering). So a computer program might treat the characters a, b, C, d, and $ as being ordered $, C, a, b, d (the corresponding ASCII codes are $ = 36, a = 97, b = 98, C = 67, and d = 100). Therefore, strings beginning with C, M, or Z would be sorted before strings with lower-case a, b, etc. This is sometimes called ASCIIbetical order. This deviates from the standard alphabetical order, particularly due to the ordering of capital letters before all lower-case ones (and possibly the treatment of spaces and other non-letter characters). It is therefore often applied with certain alterations, the most obvious being case conversion (often to uppercase, for historical reasons ) before comparison of ASCII values.

In many collation algorithms, the comparison is based not on the numerical codes of the characters, but with reference to the collating sequence – a sequence in which the characters are assumed to come for the purpose of collation – as well as other ordering rules appropriate to the given application. This can serve to apply the correct conventions used for alphabetical ordering in the language in question, dealing properly with differently cased letters, modified letters, digraphs, particular abbreviations, and so on, as mentioned above under Alphabetical order, and in detail in the Alphabetical order article. Such algorithms are potentially quite complex, possibly requiring several passes through the text.

Problems are nonetheless still common when the algorithm has to encompass more than one language. For example, in German dictionaries the word ökonomisch comes between offenbar and olfaktorisch, while Turkish dictionaries treat o and ö as different letters, placing oyun before öbür.

A standard algorithm for collating any collection of strings composed of any standard Unicode symbols is the Unicode Collation Algorithm. This can be adapted to use the appropriate collation sequence for a given language by tailoring its default collation table. Several such tailorings are collected in Common Locale Data Repository.

Sort keys
In some applications, the strings by which items are collated may differ from the identifiers that are displayed. For example, The Shining might be sorted as Shining, The (see Alphabetical order above), but it may still be desired to display it as The Shining. In this case two sets of strings can be stored, one for display purposes, and another for collation purposes. Strings used for collation in this way are called sort keys.

Issues with numbers
Sometimes, it is desired to order text with embedded numbers using proper numerical order. For example, "Figure 7b" goes before "Figure 11a", even though '7' comes after '1' in Unicode. This can be extended to Roman numerals. This behavior is not particularly difficult to produce as long as only integers are to be sorted, although it can slow down sorting significantly. For example, Microsoft Windows does this when sorting file names.

Sorting decimals properly is a bit more difficult, because different locales use different symbols for a decimal point, and sometimes the same character used as a decimal point is also used as a separator, for example "Section 3.2.5". There is no universal answer for how to sort such strings; any rules are application dependent.

Labeling of ordered items
In some contexts, numbers and letters are used not so much as a basis for establishing an ordering, but as a means of labeling items that are already ordered. For example, pages, sections, chapters, and the like, as well as the items of lists, are frequently "numbered" in this way. Labeling series that may be used include ordinary Arabic numerals (1, 2, 3, ...), Roman numerals (I, II, III, ... or i, ii, iii, ...), or letters (A, B, C, ... or a, b, c, ...). (An alternative method for indicating list items, without numbering them, is to use a bulleted list.)

When letters of an alphabet are used for this purpose of enumeration, there are certain language-specific conventions as to which letters are used. For example, the Russian letters Ъ and Ь (which in writing are only used for modifying the preceding consonant), and usually also Ы, Й, and Ё, are omitted. Also in many languages that use extended Latin script, the modified letters are often not used in enumeration.

title: Collation


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Civil Rights Act

Civil Rights Act may refer to several acts of the United States Congress, including:
 * Civil Rights Act of 1866, extending the rights of emancipated slaves by stating that any person born in the United States regardless of race is an American citizen
 * Civil Rights Act of 1871, prohibiting race-based violence against African Americans (see also Enforcement Acts, three Acts in 1870–71)
 * Civil Rights Act of 1875, prohibiting discrimination in "public accommodations", which was found unconstitutional in 1883 as Congress could not regulate conduct of individuals
 * Civil Rights Act of 1957, establishing the Civil Rights Commission
 * Civil Rights Act of 1960, establishing federal inspection of local voter registration polls
 * Civil Rights Act of 1964, prohibiting discrimination based on race, color, religion, sex, and national origin by federal and state governments as well as public places
 * Civil Rights Act of 1968, prohibiting discrimination in sale, rental, and financing of housing based on race, creed, and national origin
 * Civil Rights Act of 1990, a bill that would have made it easier for plaintiffs to win civil rights cases; was vetoed by President George H. W. Bush
 * Civil Rights Act of 1991, providing the right to trial by jury on discrimination claims and introducing the possibility of emotional distress damages, while limiting the amount that a jury could award

title: Civil Rights Act


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Cola

Cola is a carbonated soft drink flavored with vanilla, cinnamon, citrus oils, and other flavorings. Cola became popular worldwide after the American pharmacist John Stith Pemberton invented Coca-Cola, a trademarked brand, in 1886, which was imitated by other manufacturers. Most colas originally contained caffeine from the kola nut (Cola acuminata), leading to the drink's name, though other sources of caffeine are generally used in modern formulations. The Pemberton cola drink also contained a coca plant extract. His non-alcoholic recipe was inspired by the coca wine of pharmacist Angelo Mariani, created in 1863.

Most modern colas have a dark caramel color and are sweetened with sugar and/or high-fructose corn syrup. They come in numerous different brands, with Coca-Cola and Pepsi being among the most popular. These two companies have been competing since the 1890s, a rivalry that has intensified since the 1980s.

Flavorings
The primary modern flavorings in a cola drink are citrus oils (from orange, lime, and lemon peels), cinnamon, vanilla, and an acidic flavorant. Manufacturers of cola drinks add trace flavorings to create distinctive tastes for each brand. Trace flavorings may include a wide variety of ingredients, such as spices like nutmeg or coriander. Acidity is often provided by phosphoric acid, sometimes accompanied by citric or other isolated acids. Coca-Cola's recipe is maintained as a corporate trade secret.

A variety of different sweeteners may be used in cola, often influenced by local agricultural policy. High-fructose corn syrup (HFCS) is predominantly used in the United States due to the lower cost of government-subsidized corn. In Europe, however, HFCS is subject to production quotas designed to encourage the production of sugar; sugar is thus preferentially used to sweeten sodas. In addition, stevia or an artificial sweetener may be used; "sugar-free" or "diet" colas typically contain artificial sweeteners only.

In Japan, there is a burgeoning craft cola industry, with small-scale local production methods and highly unique cola recipes using locally sourced fruits, herbs, and spices.

Clear cola
In the 1940s, Coca-Cola produced White Coke at the request of Marshal of the Soviet Union Georgy Zhukov.

Clear colas were again produced during the clear craze of the early 1990s. Brands included Crystal Pepsi, Tab Clear, and 7 Up Ice Cola. Crystal Pepsi was repeatedly reintroduced in the 2010s.

In Denmark, a popular clear cola was made by the Cooperative FDB in 1976. It was especially known for being the "Hippie Cola" because of the focus on the harmful effects the color additive could have on children and the boycott of multinational brands. It was inspired by a campaign on harmful additives in Denmark by the Environmental-Organization NOAH, an independent Danish division of Friends of the Earth. This was followed up with a variety of sodas without artificial coloring. Today many organic colas are available in Denmark, but, for nostalgic reasons, clear cola has still maintained its popularity to a certain degree.

In June 2018, Coca-Cola introduced Coca-Cola Clear in Japan.

Health effects
A 2007 study claimed that consumption of colas, both those with natural sweetening and those with artificial sweetening, was associated with an increased risk of chronic kidney disease. The phosphoric acid used in colas was thought to be a possible cause.

One 2005 study indicated soda and sweetened drinks are the main source of calories in the American diet and that of those who drink more sweetened drinks, obesity rates were higher. Most nutritionists advise that Coca-Cola and other soft drinks can be harmful if consumed excessively, particularly to young children whose soft drink consumption competes with, rather than complements, a balanced diet. Studies have shown that regular soft drink users have a lower intake of calcium, magnesium, vitamin C, riboflavin, and vitamin A.

The drink has also aroused criticism for its use of caffeine, which can cause physical dependence (caffeine dependence), and can reduce sleep quality. A link has been shown between long-term regular cola intake and osteoporosis in older women (but not men). This was thought to be due to the presence of phosphoric acid, and the risk for women was found to be greater for sugared and caffeinated colas than diet and decaffeinated variants, with a higher intake of cola correlating with lower bone density.

Many soft drinks in North America are sweetened mostly or entirely with high-fructose corn syrup, rather than sugar. Some nutritionists caution against the consumption of corn syrup because it may aggravate obesity and type-2 diabetes more than cane sugar.

Asia

 * Air Koryo Cocoa Honeydew, a 'Coca-Cola-style product' manufactured by the national airline in North Korea
 * Amrat Cola, popular in Pakistan
 * Big/Real/Royal Cola, popular in Indonesia, Thailand, Nigeria and throughout South America
 * Campa Cola, India's most popular brand prior to the reintroduction of Coca-Cola and Pepsi to the Indian market in 1991
 * Chi Forest (formerly known as Genki Forest) sparkling water cola flavor, a local brand in China
 * Est Cola, a local brand in Thailand
 * Future Cola, a local brand in China
 * KIK Cola, a local brand in Sri Lanka
 * Laoshan Cola, a local brand in China
 * Mecca-Cola, sold in the Middle East, North Africa, as well as parts of Europe
 * Meadows Classic Cola, a DFI brand in Hong Kong, Malaysia, Singapore and Kampuchea
 * MyCola, a local brand in Sri Lanka
 * Pakola, popular in Pakistan
 * Parsi Cola, popular in Iran
 * Red Bull Cola, popular in Thailand
 * Sparkling Super Cola, sold by the A.S. Watson Group (PARKnSHOP, Watsons) of Hong Kong
 * Terelj Cola, sold in Mongolia.
 * Thums Up, popular in India
 * Topsia Cola, popular in Iran
 * Vita Cola, produced by Vitasoy of Hong Kong
 * Zamzam Cola, popular in Iran and parts of the Arab world

Europe

 * Afri-Cola, a German brand, was relaunched in April 2006 with the original formulation with the higher caffeine content.
 * Baikal, a cola-like drink popular in Russia
 * Barr Cola made by A.G. Barr (the makers of the popular Irn-Bru drink) in the United Kingdom
 * Breizh Cola is a local brand from Brittany (France).
 * Brisa Cola is a local brand from Madeira, Portugal and produced by Empresa de Cervejas da Madeira.
 * Cola Turka is a local brand in Turkey
 * Cockta is a local brand from former Yugoslavia, which does not contain any caffeine or phosphoric acid.
 * Corsica Cola is a regional cola distributed by the Corsican brewery Pietra.
 * Cuba Cola is a brand from Sweden.
 * Dobry Cola, a Russian brand which replaced Coca-Cola after the departure of global companies from Russia in 2022, produced in the same factories as the original products.
 * Evoca Cola is a cola made with mineral water made by Evoca Drinks.
 * Fentimans Curiosity Cola, is an upmarket botanically brewed cola produced by Fentimans, from the UK.
 * Fritz-Kola, a cola soft drink from Hamburg, Germany, uses the highest possible concentration of caffeine for beverages allowed by German law.
 * Green Cola is a brand from Greece that is available also in Germany, Spain, Cyprus, the Baltic states, Romania, the Middle East, Slovenia etc.
 * Hofmuhl Cola is a local brand from Bavaria, made by a regional brewery.
 * Jolly Cola, which had a 40% share of the cola drink market in Denmark from the mid-1960s to the late 1980s.
 * Kofola is the primary rival to Coca-Cola and Pepsi in the Czech Republic and Slovakia, and does not contain phosphoric acid.
 * Kristal Kola is a local brand in Turkey
 * LOCKWOODS Cola, a UK cola brand introduced in the 1960s produced by Lockwoods Foods Limited at their canning factory site in Long Sutton, England, the drink is not on the market anymore, it was sold nationally and also exported.
 * Maxi-Cola was sold by Mac's Brewery in England as a rival to Coke and Pepsi. Production ended in the early 90s.
 * Polo-Cockta, a Polish brand.
 * Qibla Cola was a British cola brand active from 2003 to 2005.
 * Red Bull Simply Cola has been available throughout Europe since 2008.
 * Sinalco cola is a German cola brand sold and produced in Europe
 * Tøyen-Cola is a Norwegian cola brand, based on the open Cube cola recepie.
 * Ubuntu Cola is a fair trade cola from the United Kingdom available in parts of Western Europe.
 * Virgin Cola was popular in South Africa and Western Europe in the 1990s but has waned in availability.
 * Vita-Cola is a German cola brand with a distinct citrus flavor; nowadays it is mostly sold in eastern Germany.
 * XL Cola was a Swedish cola brand introduced in 1985, but the drink is not at the market anymore.

North America

 * Coca-Cola, often referred to simply as Coke, is produced and manufactured by The Coca-Cola Company. It is one of the most popular cola brands in North America and worldwide, as well as being the original cola.
 * Pepsi, produced and manufactured by PepsiCo, is also one of the most popular cola brands in North America and worldwide. Pepsi is the main competitor and rival of Coca-Cola.
 * RC Cola, short for Royal Crown Cola, is now produced by Keurig Dr Pepper
 * Cott produces many house brand beverages as well as its own line of products, most notably its Black Cherry and Bubba cola.
 * The Double Cola Company, Double Cola
 * Faygo Cola is distributed in the Eastern United States and can be found in some regions of Canada.
 * Fentimans Curiosity Cola, originating from the United Kingdom in 1905, now sold across Europe and North America
 * Jarritos Cola is a brand of cola from Mexico, native to Mexico and widely distributed to Latino residents of the United States.
 * Jolt Cola is sold by Wet Planet Beverages of Rochester, New York.
 * Jones Soda also makes a cola using cane sugar.
 * Nuka-Cola, produced by Jones in collaboration with Fallout series developer Bethesda Softworks and Target Stores from 2009 to 2010, 2014 to 2016 and 2020 to present.
 * Polar Beverages of Worcester, MA produces its own brand of cola under the Polar name.
 * Red Bull Simply Cola was available in the United States from 2008 to 2011.
 * Shasta Cola, produced by Shasta
 * TuKola and Tropicola are brands from Cuba (also sold widely in Italy).
 * Zevia Cola is a zero-calorie soft drink sweetened with Stevia.
 * Bec Cola is produced in Montreal, Quebec, Canada, sold across Quebec and Ontario. It is sweetened with primarily maple syrup
 * Big 8 Cola is a brand of colas and other flavored sodas that can be found in Atlantic Canada

South America

 * Inca Kola, created by Lindley bottler to compete with Coca-Cola. It is still the best selling cola in Perú.
 * Big Cola, a cola produced by Peruvian company Ajegroup which operates in 14 countries in Latin America.
 * Perú Cola, created by Peruvian bottler Embotelladora Don Jorge S.A.C. to compete with Coca-Cola and Kola Real.
 * Kola Román, a cola that was invented in the city of Cartagena, Colombia in 1865 by Don Carlos Román.

Oceania

 * LA Ice Cola is an Australian cola owned by Tru Blu Beverages, similar to Coca-Cola and Pepsi, its rivals.
 * Billson's produces a Heritage Cola, inspired by recipes dating back to the Temperance movement in Australia.

Defunct brands

 * Hansen's Natural Soda, Original Cola, made with cane sugar

title: Cola


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Capability Maturity Model

The Capability Maturity Model (CMM) is a development model created in 1986 after a study of data collected from organizations that contracted with the U.S. Department of Defense, who funded the research. The term "maturity" relates to the degree of formality and optimization of processes, from ad hoc practices, to formally defined steps, to managed result metrics, to active optimization of the processes.

The model's aim is to improve existing software development processes, but it can also be applied to other processes.

In 2006, the Software Engineering Institute at Carnegie Mellon University developed the Capability Maturity Model Integration, which has largely superseded the CMM and addresses some of its drawbacks.

Overview
The Capability Maturity Model was originally developed as a tool for objectively assessing the ability of government contractors' processes to implement a contracted software project. The model is based on the process maturity framework first described in IEEE Software and, later, in the 1989 book Managing the Software Process by Watts Humphrey. It was later published as an article in 1993 and as a book by the same authors in 1994.

Though the model comes from the field of software development, it is also used as a model to aid in business processes generally, and has also been used extensively worldwide in government offices, commerce, and industry.

Prior need for software processes
In the 1980s, the use of computers grew more widespread, more flexible and less costly. Organizations began to adopt computerized information systems, and the demand for software development grew significantly. Many processes for software development were in their infancy, with few standard or "best practice" approaches defined.

As a result, the growth was accompanied by growing pains: project failure was common, the field of computer science was still in its early years, and the ambitions for project scale and complexity exceeded the market capability to deliver adequate products within a planned budget. Individuals such as Edward Yourdon, Larry Constantine, Gerald Weinberg, Tom DeMarco, and David Parnas began to publish articles and books with research results in an attempt to professionalize the software-development processes.

In the 1980s, several US military projects involving software subcontractors ran over-budget and were completed far later than planned, if at all. In an effort to determine why this was occurring, the United States Air Force funded a study at the Software Engineering Institute (SEI).

Precursor
The first application of a staged maturity model to IT was not by CMU/SEI, but rather by Richard L. Nolan, who, in 1973 published the stages of growth model for IT organizations.

Watts Humphrey began developing his process maturity concepts during the later stages of his 27-year career at IBM.

Development at Software Engineering Institute
Active development of the model by the US Department of Defense Software Engineering Institute (SEI) began in 1986 when Humphrey joined the Software Engineering Institute located at Carnegie Mellon University in Pittsburgh, Pennsylvania after retiring from IBM. At the request of the U.S. Air Force he began formalizing his Process Maturity Framework to aid the U.S. Department of Defense in evaluating the capability of software contractors as part of awarding contracts.

The result of the Air Force study was a model for the military to use as an objective evaluation of software subcontractors' process capability maturity. Humphrey based this framework on the earlier Quality Management Maturity Grid developed by Philip B. Crosby in his book "Quality is Free". Humphrey's approach differed because of his unique insight that organizations mature their processes in stages based on solving process problems in a specific order. Humphrey based his approach on the staged evolution of a system of software development practices within an organization, rather than measuring the maturity of each separate development process independently. The CMM has thus been used by different organizations as a general and powerful tool for understanding and then improving general business process performance.

Watts Humphrey's Capability Maturity Model (CMM) was published in 1988 and as a book in 1989, in Managing the Software Process.

Organizations were originally assessed using a process maturity questionnaire and a Software Capability Evaluation method devised by Humphrey and his colleagues at the Software Engineering Institute.

The full representation of the Capability Maturity Model as a set of defined process areas and practices at each of the five maturity levels was initiated in 1991, with Version 1.1 being published in July 1993. The CMM was published as a book in 1994 by the same authors Mark C. Paulk, Charles V. Weber, Bill Curtis, and Mary Beth Chrissis.

Capability Maturity Model Integration
The CMM model's application in software development has sometimes been problematic. Applying multiple models that are not integrated within and across an organization could be costly in training, appraisals, and improvement activities. The Capability Maturity Model Integration (CMMI) project was formed to sort out the problem of using multiple models for software development processes, thus the CMMI model has superseded the CMM model, though the CMM model continues to be a general theoretical process capability model used in the public domain.

In 2016, the responsibility for CMMI was transferred to the Information Systems Audit and Control Association (ISACA). ISACA subsequently released CMMI v2.0 in 2021. It was upgraded again to CMMI v3.0 in 2023. CMMI now places a greater emphasis on the process architecture which is typically realized as a process diagram. Copies of CMMI are available now only by subscription.

Adapted to other processes
The CMM was originally intended as a tool to evaluate the ability of government contractors to perform a contracted software project. Though it comes from the area of software development, it can be, has been, and continues to be widely applied as a general model of the maturity of process (e.g., IT service management processes) in IS/IT (and other) organizations.

Maturity models
A maturity model can be viewed as a set of structured levels that describe how well the behaviors, practices and processes of an organization can reliably and sustainably produce required outcomes.

A maturity model can be used as a benchmark for comparison and as an aid to understanding - for example, for comparative assessment of different organizations where there is something in common that can be used as a basis for comparison. In the case of the CMM, for example, the basis for comparison would be the organizations' software development processes.

Structure
The model involves five aspects:
 * Maturity Levels: a 5-level process maturity continuum - where the uppermost (5th) level is a notional ideal state where processes would be systematically managed by a combination of process optimization and continuous process improvement.
 * Key Process Areas: a Key Process Area identifies a cluster of related activities that, when performed together, achieve a set of goals considered important.
 * Goals: the goals of a key process area summarize the states that must exist for that key process area to have been implemented in an effective and lasting way. The extent to which the goals have been accomplished is an indicator of how much capability the organization has established at that maturity level. The goals signify the scope, boundaries, and intent of each key process area.
 * Common Features: common features include practices that implement and institutionalize a key process area. There are five types of common features: commitment to perform, ability to perform, activities performed, measurement and analysis, and verifying implementation.
 * Key Practices: The key practices describe the elements of infrastructure and practice that contribute most effectively to the implementation and institutionalization of the area.

Levels
There are five levels defined along the continuum of the model and, according to the SEI: "Predictability, effectiveness, and control of an organization's software processes are believed to improve as the organization moves up these five levels. While not rigorous, the empirical evidence to date supports this belief".
 * 1) Initial (chaotic, ad hoc, individual heroics) - the starting point for use of a new or undocumented repeat process.
 * 2) Repeatable - the process is at least documented sufficiently such that repeating the same steps may be attempted.
 * 3) Defined - the process is defined/confirmed as a standard business process
 * 4) Capable - the process is quantitatively managed in accordance with agreed-upon metrics.
 * 5) Efficient - process management includes deliberate process optimization/improvement.

Within each of these maturity levels are Key Process Areas which characterise that level, and for each such area there are five factors: goals,  commitment,  ability,  measurement,  and verification. These are not necessarily unique to CMM, representing — as they do — the stages that organizations must go through on the way to becoming mature.

The model provides a theoretical continuum along which process maturity can be developed incrementally from one level to the next. Skipping levels is not allowed/feasible.

 * Level 1 - Initial: It is characteristic of processes at this level that they are (typically) undocumented and in a state of dynamic change, tending to be driven in an ad hoc, uncontrolled and reactive manner by users or events. This provides a chaotic or unstable environment for the processes. (Example - a surgeon performing a new operation a small number of times - the levels of negative outcome are not known).

 * Level 2 - Repeatable: It is characteristic of this level of maturity that some processes are repeatable, possibly with consistent results. Process discipline is unlikely to be rigorous, but where it exists it may help to ensure that existing processes are maintained during times of stress.

 * Level 3 - Defined: It is characteristic of processes at this level that there are sets of defined and documented standard processes established and subject to some degree of improvement over time. These standard processes are in place. The processes may not have been systematically or repeatedly used - sufficient for the users to become competent or the process to be validated in a range of situations. This could be considered a developmental stage - with use in a wider range of conditions and user competence development the process can develop to next level of maturity.

 * Level 4 - Managed (Capable): It is characteristic of processes at this level that, using process metrics, effective achievement of the process objectives can be evidenced across a range of operational conditions. The suitability of the process in multiple environments has been tested and the process refined and adapted. Process users have experienced the process in multiple and varied conditions, and are able to demonstrate competence.  The process maturity enables adaptions to particular projects without measurable losses of quality or deviations from specifications. Process Capability is established from this level. (Example - surgeon performing an operation hundreds of times with levels of negative outcome approaching zero).

 * Level 5 - Optimizing (Efficient):It is a characteristic of processes at this level that the focus is on continually improving process performance through both incremental and innovative technological changes/improvements. At maturity level 5, processes are concerned with addressing statistical common causes of process variation and changing the process (for example, to shift the mean of the process performance) to improve process performance. This would be done at the same time as maintaining the likelihood of achieving the established quantitative process-improvement objectives.

Between 2008 and 2019, about 12% of appraisals given were at maturity levels 4 and 5.

Critique
The model was originally intended to evaluate the ability of government contractors to perform a software project. It has been used for and may be suited to that purpose, but critics pointed out that process maturity according to the CMM was not necessarily mandatory for successful software development.

Software process framework
The software process framework documented is intended to guide those wishing to assess an organization's or project's consistency with the Key Process Areas. For each maturity level there are five checklist types:

 * {| class="wikitable"

! Type ! Description
 * Policy
 * Describes the policy contents and KPA goals recommended by the Key Process Areas.
 * Standard
 * Describes the recommended content of select work products described in the Key Process Areas.
 * Process
 * Describes the process information content recommended by the Key Process Areas. These are refined into checklists for:
 * Roles, entry criteria, inputs, activities, outputs, exit criteria, reviews and audits, work products managed and controlled, measurements, documented procedures,  training, and tools
 * Procedure
 * Describes the recommended content of documented procedures described in the Key Process Areas.
 * Level overcome
 * Provides an overview of an entire maturity level. These are further refined into checklists for:
 * Key Process Areas purposes, goals,  policies,  and standards;  process descriptions; procedures; training; tools; reviews and audits; work products; measurements
 * }
 * Level overcome
 * Provides an overview of an entire maturity level. These are further refined into checklists for:
 * Key Process Areas purposes, goals,  policies,  and standards;  process descriptions; procedures; training; tools; reviews and audits; work products; measurements
 * }
 * }

title: Capability Maturity Model