Topological AE(0)-groups

Details Topological AE(0)-groups Topological AE(0)-groups

2000-01-04

arxiv.org/abs/math/0001017v1

Mathematics

General Topology

Scientific paper

We investigate topological AE(0) -groups class of which contains the class of Polish groups as well as the class of all locally compact groups. We establish the existence of an universal AE(0) -group of a given weight as well as the existence of an universal action of AE(0) -group of a given weight on a 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 the product of Polish groups. These results are obtained by using the spectral descriptions of AE(0)-groups which are presented in Section 3.

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