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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm167-1-6,
author = {Alex Chigogidze},
title = {Topological AE(0)-groups},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {79-96},
zbl = {0983.22002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm167-1-6}
}
Alex Chigogidze. Topological AE(0)-groups. Fundamenta Mathematicae, Tome 167 (2001) pp. 79-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm167-1-6/