Topological groups have representable actions. (English) Zbl 1432.54040

Summary: This paper shows that the group of auto-homeomorphisms of a topological group can be endowed with a topology so that the resulting topological group plays, for topological groups, the role of the group of automorphisms of a group: it represents the internal actions on the given topological group.


54H11 Topological groups (topological aspects)
57S05 Topological properties of groups of homeomorphisms or diffeomorphisms
22A05 Structure of general topological groups
Full Text: DOI Euclid