Topological transformation groups and Dugundji compacta

Topological transformation groups and Dugundji compacta

The presence of an algebraic structure on a space, which is compatible with its topology, in many cases imposes very strong restrictions on the properties of the space itself. Conditions are found which must be satisfied by the actions in order for the phase space to be a d-space (Dugundji compactum...

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Veröffentlicht in:Sbornik. Mathematics 2010-02, Vol.201 (1)
Hauptverfasser: Kozlov, Konstantin L, Chatyrko, Vitalii A
Format: Artikel
Sprache:eng
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ALGEBRA
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
MATHEMATICAL METHODS AND COMPUTING
PHASE SPACE
TOPOLOGY
TRANSFORMATIONS
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container_title Sbornik. Mathematics
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creator Kozlov, Konstantin L
Chatyrko, Vitalii A
description The presence of an algebraic structure on a space, which is compatible with its topology, in many cases imposes very strong restrictions on the properties of the space itself. Conditions are found which must be satisfied by the actions in order for the phase space to be a d-space (Dugundji compactum). This investigation allows the range of G-spaces that are d-spaces (Dugundji compacta) to be substantially widened. It is shown that all the cases known to the authors where a G-space (a topological group, one of its quotient spaces) is a d-space can be realized using equivariant maps. Bibliography: 39 titles.
doi_str_mv 10.1070/SM2010V201N01ABEH004067;COUNTRYOFINPUT:INTERNATIONALATOMICENERGYAGENCY(IAEA)
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subjects ALGEBRA
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
MATHEMATICAL METHODS AND COMPUTING
PHASE SPACE
TOPOLOGY
TRANSFORMATIONS
title Topological transformation groups and Dugundji compacta
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