scholarly journals On the topological dimension of the Gromov boundaries of some hyperbolic Out(FN)-graphs

2020 ◽  
Vol 308 (1) ◽  
pp. 1-40
Author(s):  
Mladen Bestvina ◽  
Camille Horbez ◽  
Richard D. Wade
Keyword(s):  
Topological Dimension

scholarly journals Political topology of Europe

2019 ◽  
pp. 71-93
Author(s):  
Remigiusz Rosicki
Keyword(s):  
Comparative Analysis ◽  
Civil Liberties ◽  
Geographical Area ◽  
Special Kind ◽  
Research Problem ◽  
Topological Dimension ◽  
Political Actors ◽  
Specific Geographical Area ◽  
Research Questions ◽  
Selection Of

The objective scope of the analysis performed in the text encompasses selected aspects of policy in its topological dimension. The space of policy is understood as both a theoretical construct (a policy field) and relations between the characteristics of political actors and their special kind of geographical co-existence. The following have been recognised as essential characteristics of policymaking: (1) electoral process and pluralism, (2) functioning of government, (3) political participation, (4) political culture and (5) civil liberties. These features can become an object of analysis in the assessment of democratic and authoritarian tendencies in selected countries. The text uses two statistical methods of multidimensional comparative analysis (Ward’s method and k-means method), apart from which use has been made of basic descriptive statistics and a comparative analysis of the values of the parameters of political characteristics. A selection of 40 European countries (EU-28 and 12 other countries) have been subjected to a statistical analysis according to the 2018 data. The main goal of the analysis is to connect facts and characteristics attributed to policy with a specific geographical area. In order to elaborate the objective scope of the research problem, the following research questions have been presented in the text: (1) Which of the characteristics of policy will determine the division of state entities according to a special type of clusters?, (2) Will political characteristics determine the division of particular state entities according to a special type of geographical division? The addressed research questions have been related to the hypotheses subjected to verification in the text.

A Characterization of the Topological Dimension

1982 ◽  
Vol 25 (4) ◽  
pp. 487-490
Author(s):  
Gerd Rodé
Keyword(s):  
Hausdorff Space ◽  
The Other ◽  
Natural Numbers ◽  
Topological Dimension ◽  
Other Hand ◽  
The One

AbstractThis paper gives a new characterization of the dimension of a normal Hausdorff space, which joins together the Eilenberg-Otto characterization and the characterization by finite coverings. The link is furnished by the notion of a system of faces of a certain type (N1,..., NK), where N1,..., NK, K are natural numbers. It is shown that a space X contains a system of faces of type (N1,..., NK) if and only if dim(X) ≥ N1 + … + NK. The two limit cases of the theorem, namely Nk = 1 for 1 ≤ k ≤ K on the one hand, and K = 1 on the other hand, give the two known results mentioned above.

scholarly journals On groups whose actions on finite-dimensional CAT(0) spaces have global fixed points

2019 ◽  
Vol 22 (6) ◽  
pp. 1089-1099
Author(s):  
Motoko Kato
Keyword(s):  
Fixed Points ◽  
Topological Dimension ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Thompson’S Group ◽  
Simple Action ◽  
Cube Complexes

Abstract We give a criterion for group elements to have fixed points with respect to a semi-simple action on a complete CAT(0) space of finite topological dimension. As an application, we show that Thompson’s group T and various generalizations of Thompson’s group V have global fixed points when they act semi-simply on finite-dimensional complete CAT(0) spaces, while it is known that T and V act properly on infinite-dimensional CAT(0) cube complexes.

Fractal bet and FHH theories of adsorption: a comparative study

1989 ◽  
Vol 423 (1864) ◽  
pp. 169-188 ◽  
Keyword(s):  
Critical Evaluation ◽  
Power Laws ◽  
Wall Effects ◽  
Topological Dimension ◽  
Multilayer Adsorption ◽  
High Coverage ◽  
Adsorbed Phase ◽  
Bet Isotherm ◽  
Adsorption Of Gases ◽  
Bet Theory

Two theories of multilayer adsorption of gases, namely the BrunauerEmmett-Teller (bet) theory and the Frenkel-Halsey-Hill (fhh) theory, have recently been extended to the case of fractal substrates in a number of different ways. We present a critical evaluation of the various predictions. The principal results are the following. At high coverage, the fractal bet and fhh isotherms apply to mass and surface fractals, respectively. Both give characteristic power laws with D -dependent exponents ( D = fractal dimension of the substrate). The bet isotherm additionally depends on the topological dimension D top of the substrate. For fractal aggregates ( D top = 1) with D < 2, the adsorbed phase exists only in a highly disordered state. The bet theory is sensitive to multiple-wall effects (they affect prefactors); the fhh theory is not. For the fhh theory, detailed assessments of the approximations in the model are available. The predictions of the fhh theory have been observed on fractal silver surfaces.

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