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## Fundamenta Mathematicae

2001 | 167 | 1 | 79-96

## Topological AE(0)-groups

EN

### Abstrakty

EN
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.

79-96

wydano
2001

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