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.
"Topological groups have representable actions." Bull. Belg. Math. Soc. Simon Stevin 26 (4) 519 - 526, november 2019. https://doi.org/10.36045/bbms/1576206354