# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Topological ${\rm AE} (0)$-groups

### Tom 167 / 2001

Fundamenta Mathematicae 167 (2001), 79-96 MSC: Primary 22A05; Secondary 22F05. DOI: 10.4064/fm167-1-6

#### Streszczenie

We investigate topological $\mathop {\rm AE}\nolimits (0)$-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 $\mathop {\rm AE}\nolimits (0)$-group of a given weight as well as the existence of a universal action of an $\mathop {\rm AE}\nolimits (0)$-group of a given weight on an $\mathop { \rm AE}\nolimits (0)$-space of the same weight. A complete characterization of closed subgroups of powers of the symmetric group $S_{\infty }$ is obtained. It is also shown that every $\mathop {\rm AE}\nolimits (0)$-group is Baire isomorphic to a product of Polish groups. These results are obtained by using the spectral descriptions of $\mathop { \rm AE}\nolimits (0)$-groups which are presented in Section~3.

#### Autorzy

• Alex ChigogidzeDepartment of Mathematics and Statistics