Admissible topologies for groups of homeomorphisms and substitutions of groups of G-spaces

被引：2

作者：

Karassev, A. ^{[1
]}

Kozlov, K. L. ^{[2
]}

机构：

[1] Nipissing Univ, Dept Comp Sci & Math, 100 Coll Dr,POB 5002, North Bay, ON P1B 8L7, Canada

[2] Moscow MV Lomonosov State Univ, Fac Mech & Math, Dept Gen Topol & Geometry, Moscow 119991, Russia

来源：

TOPOLOGY AND ITS APPLICATIONS | 2020年 / 275卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Homogeneity; Topological group; G-space; Uniformity; Completion;

D O I：

10.1016/j.topol.2019.107033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present approaches to substitute the acting groups of G-spaces that preserve various properties of actions, such as transitivity, being a coset space, and preserving a fixed equiuniformity in case of a G-Tychonoff space. Such substitutions make it possible to obtain bounds on cardinal invariants of acting groups with admissible topologies, and to investigate metrizability of phase spaces and find their equivariant completions of the same weight. (c) 2020 Elsevier B.V. All rights reserved.

引用

页数：17

共 50 条

[1] Groups of binary operations and binary G-spaces
Gevorgyan, P. S.
[J]. TOPOLOGY AND ITS APPLICATIONS, 2016, 201 : 18 - 28
[2] EULER CHARACTERISTICS OF DISCRETE GROUPS AND G-SPACES
BROWN, KS
[J]. INVENTIONES MATHEMATICAE, 1974, 27 (03) : 229 - 264
[3] SYNDETIC SUBMEASURES AND PARTITIONS OF G-SPACES AND GROUPS
Banakh, Taras
Protasov, Igor
Slobodianiuk, Sergiy
[J]. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2013, 23 (07) : 1611 - 1623
[4] GROUPS OF GENERALIZED ISOTOPIES AND GENERALIZED G-SPACES
Gevorgyan, P. S.
Iliadis, S. D.
[J]. MATEMATICKI VESNIK, 2018, 70 (02): : 110 - 119
[5] R-factorizability of topological groups and G-spaces
Martyanov, E. V.
[J]. TOPOLOGY AND ITS APPLICATIONS, 2023, 329
[6] Substitutional Lemma for G-spaces of 1-dimensional groups
Perez, JA
[J]. GLASGOW MATHEMATICAL JOURNAL, 1996, 38 : 215 - 220
[7] The covering number of the difference sets in partitions of G-spaces and groups
Banakh, Taras
Fraczyk, Mikolaj
[J]. EUROPEAN JOURNAL OF MATHEMATICS, 2015, 1 (04) : 762 - 772
[8] Spheroidal groups, virtual cohomology and lower dimensional G-spaces
Browder W.
[J]. Boletín de la Sociedad Matemática Mexicana, 2017, 23 (1) : 75 - 78
[9] Universal G-spaces for proper actions of locally compact groups
Antonyan, Natella
Antonyan, Sergey A.
Varela-Velasco, Ruben D.
[J]. TOPOLOGY AND ITS APPLICATIONS, 2012, 159 (04) : 1159 - 1168
[10] On the equivariant homotopy of free abelian groups on G-spaces and G-spectra
Lima, P
[J]. MATHEMATISCHE ZEITSCHRIFT, 1997, 224 (04) : 567 - 601

← 1 2 3 4 5 →