Pauline Pupier
email: pauline.pupier@gmail.com

Eurodistrict Basel

Spatial Evolution of Cross-Border Regions. Contrasted Case Studies in North-West Europe

Keywords: cross-border cooperation, cross-border region, perimeter, territorial governance, spatial evolution. Enlargement EGTC Eurodistrict Strasbourg-Ortenau

Her research investigates cross-border metropolitan regions

Introduction

Since the beginning of 1990, the territorial scope of INTERREG programmes has steadily grown. The historian Birte Wassenberg and the geographer Bernard Reitel, whose analysis of 25 years of INTERREG programmes was edited in 2015 by the European Commission, underline the progressive evolution of perimeters of crossborder cooperation. The geography of INTERREG programmes shows both a multiplication processnew programmes at new bordersand an expansion processbigger programmes' perimeters along the borders and into hinterlands. This historic perspective of growth illustrates an enthusiastic development of cross-border regions in Europe in recent decades [START_REF] Wassenberg | Territorial Cooperation in Europe -A Historical Perspective[END_REF]. The success of crossborder regions is not the only explanation for this growing trend. The shift from an experimental project to a systematic policy, the financial attraction of farther regions, the national management needs are important reasons for the increasing size of INTERREG eligibility perimeters.

By contrast, the negotiations for the forthcoming budget for the European Union (EU) in the post-Brexit area has caused anxiety amongst stakeholders of European regional development and cross-border cooperation. A so-called 'Cohesion Alliance' launched an intense lobbying action in October 2017 to ensure a strong Cohesion Policy for all regions after 2020. The challenge was to avert the European Commission's proposals to cut by 26-33% the European Structural and Investments Funds (European Commission, 2018a). Finally, the Cohesion Policy will remain the EU's most powerful investment tool over the years 2021-2027, with a budget of €330 billion, and crossborder issues will still be financially supported through a significant INTERREG programming period by €8.43 billion (European Commission, 2018b). Yet this event reveals on the one hand the kind of instability and insecurity cross-border regions must deal with in their strategies and projects, and on the other hand their resilience and adaptability in less prosperous times. We would argue that while most European crossborder regions have existed for more than 20 years, they still do not seem to be spatially stabilized, to have an enduring and clearly defined territory. In the context of European integration, cross-border regions reflect the emergence of intergovernmental territoriality. Their cross-border territory 'provides an opportunity to address mismatches between administrative and functional areas'. As such, they can be considered a form of 'soft spaces', the object of political negotiations and temporal dynamics [START_REF] Allmendinger | Europeanizing territorialitytowards soft spaces?[END_REF]. This paper aims to explore the instability and adaptability of cross-border regions from a spatial perspective. It analyses the perimeters of cross-border regions and questions their evolution. The perimeter of a cross-border region defines the bounded territorial scope on which cross-border cooperation implements a spatial strategy. The question of the limit of the perimeter is a clue to territorial construction [START_REF] Amilhat-Szary | Après les frontières, avec la frontière[END_REF]. The stability of the cross-border region perimeter is in fact crucial for any long-term spatialized policy, and especially for spatial planning. Focusing on perimeters is meaningful for further reasons: it reveals the set of local authorities involved as members of the cross-border cooperation. It is also linked to the representation of the spatial structure of the territory, and shows which spaces are consideredor consider themselvesto be border spaces. It can then be part of an identity narrative related to a cross-border territorialisation process.

In that sense, this article is rooted in political geography: it follows theories of territorial construction, arguing that cross-border regions are the outcome of a process of social and political construction [START_REF] Keating | The Invention of Regions: Political Restructuring and Territorial Government in Western Europe[END_REF][START_REF] Newman | On Borders and Power: A Theoretical Framework[END_REF][START_REF] Paasi | Foregrounding the Region[END_REF][START_REF] Perkmann | Cross-Border Regions in Europe. Significance and Drivers of Regional Cross-Border Co-operation[END_REF]. Historical, geographical or economic characteristics are instrumentalized in order to essentialize a cross-border region. Even the understanding of a border as a resource [START_REF] Sohn | Modelling Cross-Border Integration: The Role of Borders as a Resource[END_REF] means that political stakeholders mobilize it in their strategy of spatial development and territorialisation. The limits and thus the perimeter are fundamental pieces in the construction of a region [START_REF] Paasi | The Institutionalization of Regions: a Theoretical Framework for Understanding the Emergence of Regions and the Constitution of Regional Identity[END_REF]; we would argue that this is also true for cross-border regions. A methodological approach to grasp this process of territorial construction is to consider the institutionalization of cross-border cooperation [START_REF] Perkmann | Cross-Border Regions in Europe. Significance and Drivers of Regional Cross-Border Co-operation[END_REF]. Through the institutionalization process, a cross-border region will define the territorial governance [START_REF] Leloup | La gouvernance territoriale comme nouveau mode de coordination territoriale? Géographie[END_REF] that will apply within a bounded perimeter. As spatial and social objects, crossborder regions are categorized in various ways, mostly depending on their structure (natural and rural, urban or metropolitan cross-border regions), their scale (regional or local, sometimes intermediate), their institutionalization (from informal to the most complex governance structure) or on their purpose [START_REF] Durà | Euroregions, Excellence and Innovation across EU borders. A Catalogue of Good Practices[END_REF]. Some literature focuses on the spatial structure of cross-border regions. Joachim Blatter undertakes a broad comparison of cross-border cooperation in Europe with that in North America. His spatial findings reveal that 'all European institutions have defined their spatial scale of activity and developed maps to demarcate their turf', so that their geographical scales correspond to 'clear-cut definitions and congruence', whereas North American cooperation operates on 'variable and fuzzy' 'territories or networks' [START_REF] Blatter | From Spaces of Place" to "Spaces of Flows"? Territorial and Functional Governance in Cross-border Regions in Europe and North America[END_REF]. He argues that a European geography based on 'spaces of places' resulted in governance that was much more territorial than functional [START_REF] Blatter | From Spaces of Place" to "Spaces of Flows"? Territorial and Functional Governance in Cross-border Regions in Europe and North America[END_REF]. In the 2007 ESPON report, the Belgian geographer Christian Vandermotten defines Morphological Urban Areas (MUAs) and Functional Urban Areas (FUAs) all over the EU and manages to produce demographic figures and maps despite the delicate work involving non-homogenous data. Transborder FUAs are one interesting result of his typology, which identifies seven different types of transborder FUAs, depending on the continuity or discontinuities of the MUAs and FUAs across the border (ESPON, 2007). In the 2011 ESPON report entitled METROBORDER, Tobias Chilla and his Luxembourgish team examined the potential of polycentricity in a large-scale crossborder region. A qualitative analysis of the Greater Region and the Upper Region, partly commissioned by their representatives, concludes by introducing the term 'cross-border polycentric metropolitan region' (ESPON, 2010). Cross-border metropolitan regions in the EU are the subject of a recent study which investigates the relation between the centre and the periphery, and between the two national sides of the cross-border area. It puts forward a distinction between three models 'by specialization, by polarization or by osmosis' [START_REF] Decoville | Approche comparée de l'intégration métropolitaine transfrontalière en Europe[END_REF].

In addition to these comparative works, numerous case studies provide insights into the spatial structure of individual cross-border regions in Europe. It is in fact a common practice for every institutionalized cross-border region to publish a more or less solid description of its territorial scope and its self-estimated strengths and potentials. Such publications are often financed by INTERREG and reflect a politically oriented strategy rather than a scientific analysis. Yet there is a convincing example for instance in the analysis done by the Trinational Eurodistrict of Basel. Entitled Eine Zukunft zu dritt -Un Avenir à Trois ('Three sharing a future') (Eurodistrict Trinational de Bâle, 2009). A collection of academic publications applies a complementary analytical approach to individual case studies, sometimes with a thematic focus. The spatial structure of the cross-border region around Lille has for instance been studied in terms of a metropolitan approach [START_REF] Paris | Lille, de la métropole à la région urbaine[END_REF], through cross-border flows of residents [START_REF] Clément | Migrants transfrontaliers et inégalités d'accès à l'espace européen. Belgeo[END_REF], and of workers or consumers [START_REF] Letniowska-Swiat | Mobilité de la population et recomposition de l'espace périurbain: Le cas de la métropole lilloise[END_REF], through the question of the integration process [START_REF] Durand | Eurometropolis Lille-Kortrijk-Tournai: Cross-border integration with or without the border? European Urban and Regional Studies[END_REF], or through projects of urban planning [START_REF] Reitel | La resémantisation de la ligne frontière dans des régions métropolitans transfrontalières: Le jardin des 2 Rives à strasbourg et la place jacques Delors à Lille[END_REF]. Additionally, the local urban planning agency published an impressive Atlas of the cross-border Metropolitan Area of Lille (ADULM, MBM & INSEE NPdC, 2012). By comparison, the literature on some cross-border regions is more scarce. The Eurodistrict Strasbourg-Ortenau or the Franco-Belgian littoral are principally studied through the political lens of governance and institutionalization into a European Grouping of Territorial Cooperation (EGTC) (Comité des Régions, 2017;[START_REF] Fricke | Spatial Governance across Borders revisited: Organizational Forms and Spatial Planning in Metropolitan Cross-border Regions[END_REF]. The cross-border region around Strasbourg is often part of a broader analysis of the whole Upper Rhine Region [START_REF] Beck | Grenzüberschreitende Zusammenarbeit leben und erforschen[END_REF][START_REF] Beyer | La Gouvernance des transports publics comme mesure de l'intégration transfrontalière en Europe de l'ouest. L'exemple de trois Eurodistricts de Sarrebruck[END_REF][START_REF] Reitel | Les Villes, des collectivités structurantes de la région transfrontalière du Rhin supérieur[END_REF][START_REF] Wassenberg | Vers une Eurorégion? La coopération transfrontalière franco-germano-suisse dans l'espace du Rhin supérieur de 1975 à 2000[END_REF][START_REF] Woessner | Les ponts sur le Rhin dans l'espace de la Conférence du Rhin supérieur[END_REF]. Depending on the cross-border region concerned, the spatial structure of urban cross-border regions in western Europe is thus an issue on which we have unequal knowledge.

Based on these models of spatial structure and case studies, we would like to raise the question of the evolution of the territorial scope of cross-border initiatives. The aim is to grasp a subject for which it is simple enough to collect and compare data, but which is significant enough to enable discussion of the spatial evolution of cross-border cooperation in western Europe. The dynamic approach in this article might contribute to the debate on the spatial form of cross-border regions. How stable is the perimeter of a cross-border region? Can we identify specific patterns for the spatial evolution of crossborder regions? Finally, does institutionalization provide stable perimeters for crossborder regions? The first task is to check whether the multiplication and expansion of cross-border regions is as notable at EU internal borders as it is for INTERREG programmes. Our thesis is that European cross-border cooperation entered a less favourable period after its successful launch in the 1990-2000 time period. Belgium (distinguishing at the regional level between Flanders and Wallonia) in the first case, and France, Germany and Switzerland in the second case.

Following Markus Perkmann's definitions, a cross-border cooperation will be understood as 'a more or less institutionalized collaboration between contiguous subnational authorities across national borders', and a cross-border region is understood as 'a bounded territorial unit composed of the territories of authorities participating in a CBC initiative' [START_REF] Perkmann | Cross-Border Regions in Europe. Significance and Drivers of Regional Cross-Border Co-operation[END_REF]. The definition and distinction between cross-border cooperation and cross-border region are easy to operationalize and makes it possible to enumerate them in our two case studies. It allows us to perform a qualitative analysis of the perimeter of individual cross-border regions, to identify differences and similarities in their spatial evolution, and to aggregate results into patterns. Besides, we do not believe that there is any 'correct perimeter'. In a geography of places and flows [START_REF] Blatter | From Spaces of Place" to "Spaces of Flows"? Territorial and Functional Governance in Cross-border Regions in Europe and North America[END_REF][START_REF] Castells | L'Ère de l'information[END_REF], the spatial planner Noémie Hinfray even talks about 'the myth of the relevant perimeter' [START_REF] Hinfray | Les Espaces transfrontaliers, nouveaux territoires de projet, nouveaux pôles de développement au sein d'une Europe polycentrique?[END_REF]. Therefore, we cannot offer any recommendation as to what an adequate perimeter for cross-border regions would be.

The analytical matrix opens up two hypotheses (see Figure 1). The existence hypothesis deals with the number of cross-border regions. It assumes that there is a multiplication of the number of cross-border regions in our sample in western Europe (n), but that it is slowing down with time (t). The multiplication could be due to a context of intensive debate about European spatial planning [START_REF] Faludi | European Spatial Planning: Past, Present and Future[END_REF]

Existence hypothesis: multiplication of cross-border region

To verify the existence hypothesis, we count the number of distinct cross-border regions on the two borders under investigation and clarify their historical legal evolution. The criteria for this exhaustive list come from Perkmann's definition: cross-border regions operate 'in the realm of public agency', in 'a collaboration between subnational authorities', they are 'concerned with practical problem-solving' and present 'a certain stabilization' over time [START_REF] Perkmann | Cross-Border Regions in Europe. Significance and Drivers of Regional Cross-Border Co-operation[END_REF].

Multiplication: political construction processes at the British-Franco-Belgian border

Cross-border cooperation on the British-Franco-Belgian border has been studied in geographic monographs [START_REF] Hamez | Du transfrontalier au transnational: approche géographique. L'exemple de la[END_REF][START_REF] Perrin | Culture et eurorégions: la coopération culturelle entre régions européennes[END_REF][START_REF] Verger | Les chemins multiples de la coopération transfrontalière francobelge. Analyse des dynamiques institutionnelles[END_REF] and in numerous articles [START_REF] Church | Cross-border co-operation, institutionalization and political space across the English Channel[END_REF][START_REF] Duhamel | Le Détroit du Pas-de-Calais et la politique de coopération frontalière[END_REF][START_REF] Wassenberg | Vers une Eurorégion? La coopération transfrontalière franco-germano-suisse dans l'espace du Rhin supérieur de 1975 à 2000[END_REF][START_REF] Durand | Émergence d'une gouvernance métropolitaine transfrontalière au sein de l'eurométropole Lille-Kortrijk-Tournai. Analyse des relations entre les organisations dans le domaine du transport public transfrontalier[END_REF][START_REF] Durand | Binding Cross-Border Regions: An Analysis of Cross-Border Governance in Lille-Kortrijk-Tournai Eurometropolis[END_REF][START_REF] Durand | Eurometropolis Lille-Kortrijk-Tournai: Cross-border integration with or without the border? European Urban and Regional Studies[END_REF][START_REF] Heddebaut | The Euroregion from 1991 to 2020: an ephemeral stamp[END_REF][START_REF] Leloup | Le développement territorial et les systèmes complexes : proposition d'un cadre analytique[END_REF][START_REF] Maneveau | L'Eurorégion -un processus d'institutionnalisation manqué[END_REF][START_REF] Paris | Lille, de la métropole à la région urbaine[END_REF][START_REF] Perrin | La Coopération culturelle dans l'Eurorégion Nord-Transmanche: une institutionnalisation sans institution? Fédéralisme Régionalisme[END_REF]. At first sight, the British-Franco-Belgian border consists of two urban cross-border regions: the one around Lille, and the other one on the Franco-Belgian coastline.

( On the British-Franco-Belgian border, we can count five creations of different cross-border cooperations which have a clearly identified perimeter. Table 2 presents the evolution of these cross-border cooperations, distributed in three scales (local, intermediate and regional), and listed from the west to the east, and from the oldest to the newest. The British-Franco-Belgian border thus comprises five cross-border regions resulting from a process of social and political construction, as described.

Multiplication: counting cross-border regions at the Franco-German-Swiss border

The situation is much more complex on the Franco-German-Swiss border. Thanks to the work of political scientists, urbanists and historians [START_REF] Beck | Grenzüberschreitende Zusammenarbeit leben und erforschen[END_REF][START_REF] Dupeyron | Acteurs et politiques de la coopération transfrontalière en Europe[END_REF]MOT, 2007;[START_REF] Wackermann | Démarches transfrontalières pionnières sur le Rhin supérieur -Une rétrospective des débuts du façonnement d'un paysage européen du savoir[END_REF][START_REF] Wassenberg | Vers une Eurorégion? La coopération transfrontalière franco-germano-suisse dans l'espace du Rhin supérieur de 1975 à 2000[END_REF], an overview of the most significant cross-border cooperation initiatives is shown in Table 3 (listed from north to south). According to our criteria, whilst the listing claims to be exhaustive in terms of the number of cross-border cooperations and regions, it could not be exhaustive from a historical or legal point of view, due to changes of status and names.

Looking at the spatial evolution of cross-border regions, the table focuses on the creation of cross-border cooperation at a new perimeter and changes in the set of members of existing cross-border cooperation initiatives. Despite this methodological caveat, the list of potential cross-border cooperation initiatives and of their evolution is much longer for the Franco-German-Swiss border than for the British-Franco-Belgian border. And three are regional cross-border regions:

(11) The Northern Bipartite Regional Committee (12) Regio TriRhena / Southern Tripartite Regional Committee

Creation and replacement, layering, juxtaposition and scaling

The distinction made by Markus Perkmann between a cross-border cooperation and a cross-border region is very meaningful. The British-Franco-Belgian border delivers 5 cross-border cooperations in 5 cross-border regions, while the Franco-German-Swiss border delivers 22 cross-border cooperations in 13 cross-border regions.

Based on the perimeter analysis, we cannot conclude that there are as many cross-border regions as cross-border cooperations at the Franco-German-Swiss border.

For instance, the Franco-German-Swiss Intergovernmental Commission, the Franco-German-Swiss Conference, the Upper Rhine Council, the Tripartite Congresses and the Trinational Metropolitan Region all cover the same perimeter, which is called the Upper Rhine region. They are not the same cross-border cooperation, have different statuses and organizations, but they work together and pursue very similar goals for a unique territory. This phenomenon of layering also applies to other cross-border cooperations.

For most of the cases, the perimeters of the INFOBESTs coincide with the perimeters of the Eurodistricts; the Eurodistricts implement an integrated spatialized strategy while the INFOBESTs provide sectoral expertize.

In our spatial understanding, several sectoral cross-border cooperations on the same perimeter result in a single cross-border region; this is a phenomenon of layering.

A cross-border region can then include an unlimited number of cross-border cooperations. This can fuel a process of multiplication of cross-border cooperations, but maintain the number of cross-border regions at a low level. There are fewer crossborder regions than cross-border cooperations, as a region can encounter several cooperations. The geographical scope of cross-border cooperation primarily defines the cross-border region.

Both borders present indubitable activity in relation to creating and reforming cross-border cooperation. There is a real phenomenon of multiplication of cross-border cooperation. Eurocity, Eurodistrict, Euroregion, Eurometropolis… the names given to cross-border initiatives these last 50 years sound ambitious. In terms of representation, they promise flagship projects of spatial planning, innovative structures of governance or iconic visions of a future integrated territory. However, these ambitious names do not always last, and seem to belong to the trendy vocabulary of public policies. While some of these names appeared recently and others disappeared after several years, it is clear that they contribute to variable territorial marketing. Yet the diversity of names could have suggested a higher number of cross-border cooperations, but most of them are simply the result of reform of a single cross-border cooperation; a Platform becomes an EGTC, a Space becomes a Regio, an Association becomes an Eurodistrict. These events are replacements, transformations of a cross-border cooperation with the same perimeter. Thus they cannot be understood as the creation of a new cross-border cooperation.

A comparison of the two borders underlines the extreme intensity of crossborder cooperation between France, Germany and Switzerland, and a process of multiplication of cross-border regions. At this border, many phenomena of juxtaposition and scaling take place. Juxtaposition can be illustrated by the Eurodistricts which are contiguous to one another and almost cover the perimeter of the Upper Rhine region. Scaling is when a cross-border region is nested in a bigger one. For instance, the Trinational Eurodistrict of Basel lies within the perimeter of Metrobasel, which lies within the perimeter of the Regio TriRhena, which lies within the perimeter of the Upper Rhine region (see Figure 2). Cross-border regions which are in a spatial relationship of juxtaposition or scaling are independent and distinct, but very often cooperate in processes of mutual information and even in inclusive policies or projects.

A phenomenon of juxtaposition is the presence of several contiguous crossborder regions. Juxtaposition can be understood in a strict sense, as two contiguous perimeters with a shared limit, or in a wider sense, as two perimeters slightly overlapping or slightly distant. A phenomenon of scaling is a special topology of several cross-border regions which are interwoven. Due to their embedded structure, a larger cross-border region would contain one or several smaller cross-border regions.

With phenomena of juxtaposition and scaling, the multiplication of cross-border regions at a border is potentially endless.

Expansion of cross-border regions: a widespread phenomenon

Expansion of a cross-border perimeter is a very common phenomenon which can happen in slightly different situations.

Enlargement

When a new local authority joins an existing cross-border cooperation, its territory is added to the former perimeter and hence enlarges the cross-border region. We call this phenomenon enlargement, referring to the enlargement of the EU to the east.

This applied for instance to the Cross-Channel Euroregion as we saw earlier.

Another case is the Eurodistrict Strasbourg-Ortenau (see Figure 3) which took the legal Métropole Européenne de Lille with the addition of a few municipalities. Consequently, the municipalities automatically joined the Eurometropolis as it was, and adopted its cross-border cooperation acquis. In the end, the Eurometropolis Lille-Kortrijk-Tournai extended its cross-border region without any changes in membership. We call this phenomenon an expansion of an institutional logic.

On the Franco-German border, three local European districts (ED) also Figure 3). The membership remained generally unchanged (being an association, new memberships can occur smoothly), but the perimeter widened significantly. In fact, the former perimeter had been defined as an urban project territory which did not cover the whole territory of the partners. In 2001, the Association Trinational Agglomeration Basel distinguished between an inner perimeter and an expanded perimeter in its strategy. This logic is strongly influenced by functional reflections about the size of the agglomeration and the importance of economic interdependency and worker flows. The activities of the association were concentrated on the inner perimeter, while the Eurodistrict took the expanded perimeter as the new reference point. But this distinction should not be understood in a strict way. This division into perimeters is the result of years of cross-border cooperation under the flexible form of an association. It reflects a cooperation of 'variable geometry'; different partners work together on areas within the perimeter, depending on their current project. In a less administrative understanding of territoriality, the perimeter is not deduced from the members of the cross-border cooperation. This distinction is very well expressed in the German expression of Vertragsraum, the space of the parties to the contract, the institutional perimeter, and the Mandatsraum, the space of mandate, the strategic perimeter of projects (ESPON, 2010;[START_REF] Evrard | Suprarégionalisation transfrontalière? Grande Région Saar-Lor-Lux[END_REF][START_REF] Evrard | Asymétries institutionnelles et territoriales. Quelles conséquences pour la gouvernance transfrontalière[END_REF]. In the Trinational Eurodistrict Basel, the Mandatsraum is the only official perimeter, and it coincides with the cross-border region. Here Perkmann's definition does not quite fit. The cross-border region of the Trinational Eurodistrict Basel is not 'a bounded territorial unit composed of the territories of authorities participating in a [cross-border cooperation]' [START_REF] Perkmann | Cross-Border Regions in Europe. Significance and Drivers of Regional Cross-Border Co-operation[END_REF].

The flexibility of the associative structure and the pragmatic project-based approach differs from the territorial approach of the Eurometropolis Lille-Kortrijk-Tournai, for instance. This expansion took place on a functional logic.

Fusion

After enlargement and expansion, the observation of increasing evolution would not be complete without the phenomenon of fusion. The Franco-German-Swiss border offers two examples of fusion, while no counter-example of splitting could be found.

The Each of them acted on a strictly national perimeter, but they built a 'spirit of regional community' [START_REF] Wassenberg | De l'esprit "Regio" aux Eurodistricts: la place de la société civile dans la coopération transfrontalière du Rhin supérieur (1963-2008)[END_REF] thanks to cross-border cooperation around Basel. At that point, we cannot count them as cross-border regions. But in 1995, together they founded the cross-border association Regio TriRhena. In this case, the fusion is a simple creation: cross-border cooperation gets institutionalized and a new cross-border region arises. Interestingly, the perimeter of the Regio TriRhena matches the perimeter of the former Tripartite Committee.

Disappearance: a rarity

As the opposite phenomenon to multiplication and expansion, decreasing spatial evolution is very rare at both borders. Cross-border cooperation may be a delicate practice of 'micro-diplomacy' [START_REF] Wassenberg | Vers une Eurorégion? La coopération transfrontalière franco-germano-suisse dans l'espace du Rhin supérieur de 1975 à 2000[END_REF], so that criticism and disagreement would be part of the process, along with shrinkage, withdrawal and disappearance.

These decreasing phenomena could be signs of a crisis, of success or of reorganization.

Yet our research shows only one case of withdrawal followed by dissolution. This happened in the Cross-Channel Euroregion.

The Channel Tunnel was a great challenge for cross-border cooperation before According to the results of the COOP-RECOT II study, 26% of cross-border regions in Europe simply remain inactive [START_REF] Durà | Euroregions, Excellence and Innovation across EU borders. A Catalogue of Good Practices[END_REF]. Cross-border regions had been active in the past but did not show any sign of activity (no projects, no online updates, no emails and no response to contact) at the time the study was conducted. This means that a significant number of cross-border regions no longer cooperate, but they have not undertaken either withdrawal or dissolution, hence leaving their official perimeter untouched. In that sense, the Cross-Channel Euroregion constitutes an extreme case of the dissolution of a cross-border cooperation subsequent to three withdrawals. In spatial terms, it resulted in a phenomenon of disappearance subsequent to three phenomena of shrinkage. A shrinkage phenomenon is a decrease in the perimeter of a cross-border region, explained in this case by the withdrawal of a member. A cross-border region disappears when the last cross-border cooperation on its perimeter is dissolved, which means that members render the end of their cross-border cooperation official. A shrinkage is related to the evolution hypothesis of a decreasing perimeter of cross-border regions, while a disappearance is related to the existence hypothesis of a decreasing number of cross-border regions.

Barely any shrinkage phenomenon

The Mandatsraum and a Vertragsraum, but in the opposite way. In Basel, an evolution in the strategy opened up a broader territory in addition to the original small one. On the Franco-Belgian coastline, the new EGTC statutes hierarchized the original wide territory into a core territory and the rest. This soft concentration can hardly be understood as a form of shrinkage of a cross-border region.

Conclusion: patterns of spatial evolution

The analysis of cross-border perimeters on the British-Franco-Belgian and the Franco-German-Swiss border proves fruitful in terms of revealing patterns of spatial evolution (see Table 4). Cross-border cooperation and cross-border region are interconnected but not identical. This challenges the identification and definition of cross-border regions. this means that the cross-border region grows without any changes in the set of members of the cross-border cooperation. It can be due to an expanding member, or to a change in the Mandatsraum [START_REF] Evrard | Asymétries institutionnelles et territoriales. Quelles conséquences pour la gouvernance transfrontalière[END_REF] of the cross-border cooperation, i.e. the strategic perimeter of projects. The difference between the two expansion phenomena is the distinction between an administrative and a functional logic, which is conceptually based on a 'spaces of place' and 'spaces of flows' logic. According to Joachim Blatter, territorial governance would generate geographical scales with clearcut definitions and congruence, whereas functional governance would accept fuzzy geographies [START_REF] Blatter | From Spaces of Place" to "Spaces of Flows"? Territorial and Functional Governance in Cross-border Regions in Europe and North America[END_REF]. Even in the EU, where territorial governance is closely related to 'spaces of place', some cross-border regions demonstrate spatial evolution which can be linked to 'spaces of flows'. Such functional governance leads us to question Perkmann's definition with regard to its relation between cross-border cooperation and cross-border region: a cross-border region is not necessarily the sum of the perimeter of the members of the cross-border cooperation.

In opposition to the variety of increasing phenomenon, only a few case studies show decreasing trends of cross-border perimeters. The concentration phenomenon witnessed in the Franco-Belgian littoral EGTC rather corresponds to an internal reorganization. Cross-border cooperations might encounter various difficulties, but generally have no effect on cross-border regions. Only the case of the Cross-Channel

Euroregion provides an example of dramatic withdrawal and disappearance. Euroregion, the majority of cross-border regions tend to stay stable or to extend.

Answering our initial question, institutionalization of cross-border regions does provide stable perimeters at the British-Franco-Belgian border and at the Franco-German-Swiss border. The spatial evolution of cross-border regions does not indicate a crisis in crossborder cooperation in Europe. Yet we cannot conclude that spatial evolution perfectly reflects the health of cross-border cooperation. Incontestably, the diversity of phenomena of spatial evolution shows the ability of cross-border cooperations to rethink their perimeters. In that geographic sense, a cross-border region is the 'result of a process of political and social construction', but not strictly 'a bounded territorial unit composed of the territories of authorities participating in a [cross-border cooperation] initiative' [START_REF] Perkmann | Cross-Border Regions in Europe. Significance and Drivers of Regional Cross-Border Co-operation[END_REF]. The link with the perimeter of the local authorities can be loose. In a political geographical understanding, a cross-border region is the perimeter to which one or several cross-border cooperation initiatives refer, which means the bounded geographic scope on which cross-border cooperation asserts implementation of a spatial strategy.

Cross-border cooperations and regions prove to be very adaptable by adjusting their perimeters, which might preserve them from instability and disappearance. This flexibility is a privilege given to cross-border regions as 'soft spaces', which differentiates them from administrative national regions. In that sense, cross-border regions are free from 'various form of essentialism and fetishism' [START_REF] Paasi | Foregrounding the Region[END_REF] and have the opportunity to experiment in time and space. The building process of cross-border regions proves to be erratic and progressive [START_REF] Wassenberg | Vers une Eurorégion? La coopération transfrontalière franco-germano-suisse dans l'espace du Rhin supérieur de 1975 à 2000[END_REF]. Crossborder cooperation exercises creativity and flexibility and can be considered a laboratory of territorial construction in Europe. Cross-border regions contribute to the 'complex, evolving, and contested nature of reterritorialization of European space'. [START_REF] Allmendinger | Europeanizing territorialitytowards soft spaces?[END_REF].

  Our sample gathers case studies along two borders in western Europe. It consists of two geographical borders and their cross-border cooperation. Selected for their long tradition of cross-border cooperation, the British-Franco-Belgian border and the Franco-German-Swiss border offer numerous examples for our methodology. Both borders are approximately 200 kilometres long, from Dunkerque-Oostende to Maubeuge-Charleroi on the one border, and from Karlsruhe to Basel on the other border. They both show initial processes of social construction of cross-border regions before 1980. They both connect three countries: the United Kingdom across English Channel, France and

  and the financial opportunity of INTERREG programmes. The slowing down could be geographically explained by the number of potential configurations on a limited border coming to an end. The evolution hypothesis concerns the adaptation of the perimeters. It builds on the temporal dynamics of 'soft spaces'[START_REF] Allmendinger | Europeanizing territorialitytowards soft spaces?[END_REF]. It imagines a process of size fitting and experimentation in the set of members and in the perimeter. Large cross-border regions might tend to shrink, while small cross-border regions might tend to extend. Cross-border regions might experience softening or hardening of their territories.

Figure 1 .

 1 Figure 1. Hypothesis of spatial evolution.

  ) A first cross-border region lies on the Franco-Belgian coastline. In the 1970s, the Communauté urbaine de Dunkerque and the West-Vlaamse Intercommunale started informal cooperation in the fields of economic development and spatial planning. This initiative was supported by an agreement between the Département du Nord and the Provincie West-Vlaanderen in 1989. Finally, the 'Cross-Border Platform West-Vlaanderen / Flandre-Dunkerque-Côte d'Opale' was founded in 2005. In 2009, it grew into a EGTC, including all levels of government from both sides. Because they declined invitations to join the Platform and the EGTC, British partners from Kent and Dover only participate on the basis of ad hoc projects. They do not belong to this cross-border region. (2) A metropolitan cross-border region emerged around Lille and the Belgian surrounding intermunicipalities, thanks to a coalition of political leaders and economic stakeholders. Their purpose was to emerge from the shadow of London, Paris and Brussels. The cross-border cooperation was first institutionalized in 1991 through the Conference permanente intercommunale transfrontalière (COPIT), a standing cross-border conference of intermunicipal organizations. A European Economic Interest Grouping (EEIG) followed, and a Local Grouping of Cross-Border Cooperation 1 was established in 2005 under the name 'Lille Franco-Belgian Metropolis'. It turned into the very first EGTC in Europe in 2008: the 'Eurometropolis Lille-Kortrijk-Tournai'. Its territory unites the intermunicipalities of the three main cities, Lille in France, Kortrijk in Flanders (Belgium) and Tournai in Wallonia (Belgium), and results in a mixed geographical structure of an urban network with rural areas. These two cross-border regions are well known in Europe, but they hide three other cross-border regions which we must consider in our analysis of perimeter evolution: the Hainaut Cross-Border Nature Park gets less attention, the Metropolitan Area of Lille is often forgotten, and the Cross-Channel Euroregion is no longer active. (3) The Hainaut Cross-Border Nature Park comes from a memorandum of understanding signed in 1983 by the regions Wallonia and Nord-Pas-de-Calais. Projects received financial support in the INTERREG I and II periods at a time when cross-border cooperation was not institutionalized. The cross-border park was created in 1996 as a cooperation between the two pre-existing national nature parks, the Parc regional naturel Scarpe-Escaut on the French side, and the Parc naturel des Plaines de l'Escaut on the Belgian side. (4) The Metropolitan Area of Lille is a second Franco-Belgian cross-border region larger than the Eurometropolis. It must be distinguished because it does not fit into its temporal development and its territorial scope. Indeed, the COPIT signed the declaration of intent of 2005 with other members. The Metropolitan Area of Lille was created as an association in 2007. Its logic is to involve the partners of the whole functional area of the Franco-Belgian metropolis. For this reason, it covers the same Belgian area as the Eurometropolis on the northern side but a much larger area in France on the southern side. It extends to Hazebrouck, Arras, Cambrai, Valenciennes and even Maubeuge. Although the members claim to stick to the metropolitan functional area, the perimeter reveals two curiosities: Maubeuge is isolated from the rest of the territory, and the neighbouring Belgian city of Mons does not belong to the cross-border region.(5) The only cross-border region with British members is the Cross-Channel Euroregion. The high-speed train connection to the continent and the digging of the Channel Tunnel were huge construction works which provided an opportunity for cross-border cooperation. The Cross-Channel Euroregion was created in 1987 through an agreement between the region Nord-Pas-de-Calais and the county of Kent. In 1991, the three Belgian regions (Flanders, Wallonia and Brussels Capital) joined the partnership, widening the perimeter of the cross-border cooperation to the whole country. It was dissolved in 2004.It is worth discussing why other kinds of extant or previously existing crossborder cooperation are not included in this list. The cross-border theatre Le Manège in Maubeuge rather operates as a network with theatres in Mons but also in Gent and Brussels[START_REF] Perrin | La Coopération culturelle dans l'Eurorégion Nord-Transmanche: une institutionnalisation sans institution? Fédéralisme Régionalisme[END_REF]. There is no continuity of subnational authorities and therefore no cross-border region. The cross-border natural region of La Thiérache presents a lot of INTERREG projects but has never defined a proper territory or stable cooperation.Cross-border health management between France and Belgium led to definition of seven zones along the border. The so-called ZOAST (Zones Organisées d'Accès aux Soins de Santé Transfrontaliers or planned cross-border health treatment zones) indeed present cross-border territoriality, but are a case of centrally managed administrative zoning rather than institutionalized cross-border cooperation[START_REF] Delecosse | La coopération transfrontalière dans le domaine de la santé: principes et pratiques[END_REF] MOT, 2007). Such networks, projects and administrative divisions might indeed cross borders, but they were not taken into account here due to their lack of institutionalization or territoriality.

( 13 )

 13 The Upper Rhine region This result could be open to discussion, as some perimeters are very similar. For instance, one could argue that the Trinational Eurodistrict of Basel and Metrobasel are merely the same cross-border region. Another issue is the recognition of former perimeters of cross-border cooperation as cross-border regions, as in the case of the Northern Regional Committee (and of the Cross-Channel Euroregion).

Figure 2 .

 2 Figure 2. Juxtaposition and scaling: Perimeters in the Upper Rhine Region (Eurodistrict

  form of an EGTC in 2010 with one French member, the Communauté urbaine de Strasbourg, and six German members, the Landkreis Ortenaukreis, and the towns or cities of Offenburg, Lahr, Kehl, Achern and Oberkirch. In 2013, three French local authorities joined the EGTC. The Communautés de Communes du Pays d'Erstein, du Rhin et de Benfeld et environs accepted a kind of 'cross-border cooperation acquis' when they joined. Through this, the French side of the cross-border region doubled in size, softening the geographical asymmetry of the former cross-border perimeter. The Franco-Belgian littoral EGTC experienced an enlargement too. During the discussions and negotiations about the new legal form of the cross-border cooperation in 2009, the five official members of the Platform West-Vlaanderen/Flandre-Dunkerque-Côte d'Opale (Provincie West-Vlaanderen, intermunicipalities WVI, Commaunauté urbaine de Dunkerque and Pays Moulins de Flandre, and the urban planning agency AGUR) opened up the talks to other potential members in the surrounding areas. British partners kept up to date with the process but decline to join, Sociaal-Economisch Overlegcomité Westhoek, the Communauté de Communes des Hauts de Flandre and the Syndicat mixte du Pays Coeur de Flandre. This case is rather one of making official the former cross-border cooperation, and a reorganization of governance, as these members were already involved in informal decision-making of the Platform. Nevertheless, the replacement of the Platform by the EGTC resulted in a phenomenon of official enlargement of the cross-border region.

Figure 3 .

 3 Figure 3. Examples of enlargement, expansion and concentration

  experienced an expansion in 2017 due to the French territorial reform. The Eurométropole de Strasbourg integrated the Communauté de Communes des Châteaux, expanding once again the perimeter of the Eurodistrict Strasbourg-Ortenau. The French intermunicipalities Pays de Brisach and Essor du Rhin merged, even if each of them was a member of a cross-border cooperation. Consequently, the ED Pays des Deux Brisach/Zwei-Brisacher-Land and the ED Centre Hardt/Mittelhardt both expanded on their French sides. Expansion took a different course in the replacement of the Association Trinational Agglomeration Basel by the Trinational Eurodistrict Basel in 2007 (see

  Bonn agreement, signed in 1975, established three different cross-border cooperations: the Franco-German-Swiss Intergovernmental Commission covered the Upper Rhine region, the Bipartite Regional Committee lay in the north, and the Tripartite Regional Committee lay in the south (it replaced a previous Standing Tripartite Conference). After their third meeting in 1991, the two Regional Committees merged, creating the Franco-German-Swiss Conference of the Upper Rhine. This fusion means the disappearance of two cross-border regions, although cross-border cooperation still exists in a merged cross-border region. The evolution of the Regios follows a different path, as they were created separately but in a parallel way: the Regio Basiliensis in Basel in 1963, the Regio du Haut-Rhin in 1976 in Colmar, the Regio Freiburg in Freiburg im Breisgau in 1985.

  and after its opening in 1994. The members of the Cross-Channel Euroregion later cooperated in the framework of INTERREG projects. When the important project SPACE (Spatial Planning And Cities in the Euroregion) came to an end in 2000, the members began to question the goals of the cross-border cooperation. The construction work and necessary regulation linked to the Channel were over. The new connection obviously facilitated exchanges, but also strengthened economic competition. Over the course of a few months in 2001 and 2002, the three Belgian regions withdrew one after the other: Brussels Capital, then Flanders and finally Wallonia. The cross-border region has therefore progressively shrunk, losing the territory of each member as it leaves. For a few months, the cross-border region had a curiously discontinuous perimeter, with Brussels appearing as a hole. The office of the Euroregion had to leave Etterbeek-Brussels for Lille in 2002. The French and British attempted to build new bilateral projects in the field of tourism, and introduced the name 'Cross-Channel Region'. On 4 June 2003, the liquidation of the EEIG Euroregion was ongoing and an extraordinary general assembly with representatives from the five regional members voted for the dissolution of the Cross-Channel Euroregion. This cross-border region disappeared.

  Trinational Eurodistrict Basel presents the only other example of a shrinking crossborder region. The French municipality of Steinbrunn-le-Bas is located at the northwest limit of the Trinational Eurodistrict Basel. In 2013, it decided to join the newly created Mulhouse Alsace Agglomeration and consequently left the Communauté de Communes de Sierentz, which is part of the TEB perimeter. The reason for this shrinkage phenomenon is rather a pull factor, in sense of the attraction of the Mulhouse urban area, than a push factor, in the sense of a withdrawal from the Trinational Eurodistrict Basel. Nevertheless, it resulted in a small shrinkage of the cross-border region (see Figure3).Apart from the very singular case of the Cross Channel Euroregion and the small shrinkage of the Trinational Eurodistrict of Basel, almost no cross-border regions experienced a shrinkage or a disappearance. Disagreements and conflict certainly occur in cross-border cooperation, without leading to spatial evolution of the perimeter.In the Upper Rhine region, the southern cantons regularly express criticism of the low efficiency of cross-border cooperation compared to the multiplicity of institutions. The cantons of Aargau, Solothurn and Jura call for more pragmatism and project realization. They joined the Franco-German-Swiss Conference of the Upper Rhine quite recently, with the Basel Agreement of 2000. However, the criticism mainly aims to achieve improvement, and no withdrawal is on the agenda.On the British-Franco-Belgian border, the EGTC Eurometropolis faced an important crisis in 2015, in which the representative did not attend the meetings, the assembly could not make decisions, other decision-making bodies did not work. The whole board of directors resigned, the strategy was put on hold and questions about the future of the Eurometropolis were raised. Nevertheless, no member of the cross-border cooperation has left, and the cross-border region has remained the same. Amongst other members, the Mayors of Lille, Kortrijk and Tournai committed to continue the crossborder cooperation in the Eurometropolis. New statutes were signed in 2017 and a new direction reorganized work in the agency. Such political momentum rather consists in an internal reorganization which seems to be part of the construction process of a crossborder region.Whilst shrinkage in the form of a withdrawing member happened only in the Cross-Channel Euroregion, we looked for other potential types of shrinkage. The only case we could refer to here is a phenomenon of concentration in the Franco-Belgian littoral EGTC (see Figure3). At the creation of the littoral EGTC, the members defined a two-scale territory. A core territory includes the border areas, on the French and Belgian sides, from the coastline to the hinterlands. More distant areas like Kortrijk, Calais or Boulogne are included in the periphery of the EGTC West-Vlaanderen/Flandre-Dunkerque-Côte d'Opale. This evolution recalls the functional logic of the case of the Trinational Eurodistrict of Basel and the distinction between a

Figure 4 .

 4 Figure 4. Multiplication of cross-border cooperation initiatives and cross-border regions

Figure 5 .

 5 Figure 5. Patterns of spatial evolution in cross-border regions

Table 1 .

 1 Analytical matrix for spatial evolution.

			Temporality
			Existence	Evolution
	Dynamics	Increase Decrease	Multiplication Disappearance	Expansion Shrinkage
		Based on the results obtained by Birte Wassenberg and Bernard Reitel
	(Wassenberg et al., 2015), we developed an analytical matrix of possible spatial
	evolution (see Table 1). The analytical matrix covers two temporal dimensions
	(existence and evolution) and two dynamic dimensions (increase and decrease). Trends
	of multiplication and expansion were noticeable for INTERREG programmes, but do
	they also apply for every cross-border region? Are they not the opposite phenomena of
	disappearing and shrinking? This assumption is supported by the results of the project
	COOP-RECOT II. The geographers from the Universitat Autònoma de Barcelona put
	together an exhaustive database of what they call 'Euroregions' in Europe. 'From a total
	214 Euroregions, 158 were active and 56 were inactive' (Durà et al., 2018). This
	proportion of 26% of Euroregions that were inactive might have experienced decreasing
	phenomena of disappearance or shrinkage.
		The observation of increase and decrease phenomena should not lead to
	normative misunderstandings. Our analysis does not argue 'the more, the better' or 'the
	bigger, the better'. Besides, an increasing trend does not necessarily mean
	'debordering', nor does a decreasing trend mean 'rebordering' (Van Houtum, Kramsch,

Table 2 .

 2 Overview of spatial evolution of cross-border regions on the British-Franco-

	Belgian border
	Date	Name	Spatial evolution
	Local scale
	1991	Conférence permanente	Creation
		intercommunale transfrontalière
		COPIT
	2005	ED Lille Franco-Belgian	Unchanged
		Metropolis
	2008	EGTC Eurometropolis Lille-	Unchanged
		Kortrijk-Tournai
	1996	Cross-border Nature Park Hainaut	Creation
	Intermediate scale
	2005	Cross-Border Platform West-	Creation
		Vlaanderen/Flandre-Dunkerque-
		Côte d'Opale
	2009	EGTC West-Vlaanderen/Flandre-	Enlargement and concentration
		Dunkerque-Côte d'Opale
	2007	Metropolitan Area of Lille	Creation
	Regional scale
	1987	Euroregion	Creation
	1991	EEIG Cross-Channel Euroregion	Enlargement
	2001-2002 Cross-Channel Region	Withdrawing partners
	2004	Dissolution	Dissolution

Table 3 .

 3 Overview of spatial evolution of cross-border regions on the Franco-German-The INFOBEST and the Euro-institute provide cross-border expertize to enterprises, citizens and local authorities from a bounded territory, and they are supported and financed by public authorities. Metrobasel could be a controversial example because it was created as a public-private association, but its objective is still the development of an integrated trinational metropolitan region around Basel involving all types of stakeholders, from local authorities and associations to companies and individual citizens. The Trinational Metropolitan Region of the Upper Rhine joined the list even if it is an emanation of the Franco-German-Swiss Conference and of the Tripartite Congress. It could be interpreted as a labelling and branding policy within existing cross-border cooperation, but the fact that is has existed for 10 years, and that dedicated staff regularly work for it in different institutions (pillars), made the difference. By contrast, the list does not contain the Regio Basiliensis (or the other national Regio), although it has been promoting cross-border cooperation since 1963.

	Swiss border
	Date	Name	Perimeter
	Local scale
		ED Wissembourg-Bad Bergzabern	Creation
		Joint municipal Council in Strasbourg	Creation
		and Kehl
		Commission Strasbourg-Kehl	Unchanged
		ED Vis à Vis	Creation
		ED Pays des Deux Brisach/Zwei-	Creation
		Breisacher-Land
			Expansion
		ED Centre Hardt/Mittelhardt	Creation
			Expansion
		Trinational Agglomeration Basel	Creation
		Association Trinational Agglomeration	Unchanged
		Basel
		Trinational Eurodistrict Basel	Expansion
			Shrinking
	Intermediate scale
		PAMINA Space	Creation
		Regio PAMINA	Unchanged
			Expansion
		ED Eurodistrict Regio PAMINA	Unchanged
		INFOBEST PAMINA	Creation
		INFOBEST Kehl-Strasbourg	Creation
		EEIG Euro-institute Kehl-Strasbourg	Creation
		Eurodistrict Strasbourg-Ortenau	Creation
		EGTC Eurodistrict Strasbourg-Ortenau Unchanged
			Enlargement
		Communauté d'Intérêt Moyenne	Creation
		Alsace-Breisgau
		Eurodistrict Region Freiburg -Centre	Unchanged
		et Sud Alsace
		INFOBEST Vogelgrun-Breisach	Creation

But it is difficult to call it cross-border itself, as it represents the Swiss cantons in different matters and in several cross-border institutions. The Euroairport Basel-Mulhouse or the joint administration of the port of Kehl is not cross-border regions, as they are not clearly bounded territorial units.

In total, the Franco-German-Swiss border delivers no less than 22 creations of cross-border cooperation. To sum up, our methodology yields 13 different perimeters of cross-border cooperation, resulting in 13 different cross-border regions on the

Table 4 .

 4 Spatial evolution of cross-border cooperation and cross-border regions Regarding the multiplication of cross-border cooperation, a replacement is the transformation of a cross-border cooperation by a new one on the same perimeter. It does not affect the cross-border region, as the territorial scope remains unchanged. A layering is a superposition of several cross-border cooperations on a single cross-border region. It results in only one cross-border region. Regarding the multiplication of crossborder regions, juxtaposition is when two cross-border regions are contiguous one to another. Scaling is when a cross-border region is nested in a bigger one. Topological relations of cross-border regions such as layering, juxtaposition and scaling explain how the number of cross-border cooperations and cross-border regions can continue to grow. Since 2000, a normalization process has taken into account the normative and regulatory function of even open borders, and cross-border cooperation replaces symbolic projects with a more realistic management.

	Temporality
	Existence	Evolution

period of naïve cross-border euphory -Stefanie Dühr and Phil Allmendinger refer to 'hype' in this regard

[START_REF] Allmendinger | Europeanizing territorialitytowards soft spaces?[END_REF][START_REF] Dühr | European Spatial Planning and Territorial Cooperation[END_REF]

.

This legal form comes from the Karlsruhe Agreement and has been renamed 'European district' or 'ED'.

This work was supported by the Collège doctoral Lille-Nord-de-France under Grant for International Mobility [numbers 14 and 16], the Conseil Régional du Nord-Pas-de-Calais and the Université d'Artois under Grant for doctoral research.