Topological AE(0)-groups

Alex Chigogidze

Fundamenta Mathematicae (2001)

  • Volume: 167, Issue: 1, page 79-96
  • ISSN: 0016-2736

Abstract

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We investigate topological AE(0)-groups, a class which contains the class of Polish groups as well as the class of all locally compact groups. We establish the existence of a universal AE(0)-group of a given weight as well as the existence of a universal action of an AE(0)-group of a given weight on an AE(0)-space of the same weight. A complete characterization of closed subgroups of powers of the symmetric group S ∞ is obtained. It is also shown that every AE(0)-group is Baire isomorphic to a product of Polish groups. These results are obtained by using the spectral descriptions of AE(0)-groups which are presented in Section 3.

How to cite

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Alex Chigogidze. "Topological AE(0)-groups." Fundamenta Mathematicae 167.1 (2001): 79-96. <http://eudml.org/doc/282368>.

@article{AlexChigogidze2001,
abstract = {We investigate topological AE(0)-groups, a class which contains the class of Polish groups as well as the class of all locally compact groups. We establish the existence of a universal AE(0)-group of a given weight as well as the existence of a universal action of an AE(0)-group of a given weight on an AE(0)-space of the same weight. A complete characterization of closed subgroups of powers of the symmetric group $S_\{∞\}$ is obtained. It is also shown that every AE(0)-group is Baire isomorphic to a product of Polish groups. These results are obtained by using the spectral descriptions of AE(0)-groups which are presented in Section 3.},
author = {Alex Chigogidze},
journal = {Fundamenta Mathematicae},
keywords = {topological -group; Polish group; inverse spectrum; AE(0)-groups; inverse spectra},
language = {eng},
number = {1},
pages = {79-96},
title = {Topological AE(0)-groups},
url = {http://eudml.org/doc/282368},
volume = {167},
year = {2001},
}

TY - JOUR
AU - Alex Chigogidze
TI - Topological AE(0)-groups
JO - Fundamenta Mathematicae
PY - 2001
VL - 167
IS - 1
SP - 79
EP - 96
AB - We investigate topological AE(0)-groups, a class which contains the class of Polish groups as well as the class of all locally compact groups. We establish the existence of a universal AE(0)-group of a given weight as well as the existence of a universal action of an AE(0)-group of a given weight on an AE(0)-space of the same weight. A complete characterization of closed subgroups of powers of the symmetric group $S_{∞}$ is obtained. It is also shown that every AE(0)-group is Baire isomorphic to a product of Polish groups. These results are obtained by using the spectral descriptions of AE(0)-groups which are presented in Section 3.
LA - eng
KW - topological -group; Polish group; inverse spectrum; AE(0)-groups; inverse spectra
UR - http://eudml.org/doc/282368
ER -

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