The dual space of precompact groups

Commentationes mathematicae Universitatis Carolinae

M. Ferrer¹ 

关键词: compact group;    precompact group;    representation;    Pontryagin--van Kampen duality;    compact-open topology;    Fell dual space;    Fell topology;    Kazhdan property (T);   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

For any topological group $G$ the dual object $\widehat G$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\widehat G$ is discrete. In an earlier paper we proved that $\widehat G$ is discrete for every metrizable precompact group, i.e.~a dense subgroup of a compact metrizable group. We generalize this result to the case when $G$ is an almost metrizable precompact group.

【 授权许可】

CC BY