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Topological AE(0)-groups

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Chigogidze A.

Fundamenta Mathematicae

2001

tom 167

nr 1

79-96

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.

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1 Fundamenta Mathematicae

1 Chigogidze A.

1 2001

Wyniki wyszukiwania

Topological AE(0)-groups