The weights of closed subgroups of a locally compact group

Abstract

Abstract. Let G be an infinite locally compact group and let @ be a cardinal satisfying

Unbounded actions of metric groups and continuous logic

“…Remark We mention the paper [21] where related questions were studied in the case of locally compact groups. It is proved in [21] that for any locally compact group G , the entire interval of cardinalities between ℵ 0 and , the weight of the group, is occupied by the weights of closed subgroups of G .…”

“…Remark We mention the paper [21] where related questions were studied in the case of locally compact groups. It is proved in [21] that for any locally compact group G , the entire interval of cardinalities between ℵ 0 and , the weight of the group, is occupied by the weights of closed subgroups of G . We remind the reader that the weight of a topological space is the smallest cardinality which can be realized as the cardinality of a basis of .…”

Nonmeasurable subgroups of compact groups

“…In [10], Corollary 1.2 we noted that every uncountable abelian group has a proper subgroup H of countable index. (See also [11] Here is a partial answer to Question 1:…”

Metric groups, unitary representations and continuous logic

“…In this paper we study the behavior of amenability and Kazhdan's property (T) under logical constructions. We view these tasks as a part of investigations of properties of basic classes of topological groups appeared in measurable and geometric group theory, see [9], [10], [13]. The fact that some logical constructions, for example ultraproducts, have become common in group theory, gives additional flavour for this topic.…”