Coset spaces of metrizable groups
Volume 167 / 2022
Colloquium Mathematicum 167 (2022), 1-20
MSC: Primary 54H15, 22F30; Secondary 54D35, 57S05.
DOI: 10.4064/cm7963-8-2020
Published online: 15 March 2021
Abstract
We characterize topological spaces which are coset spaces of (separable) metrizable groups and complete metrizable (Polish) groups. Moreover, it is shown that for a $G$-space $X$ with a $d$-open action there is a topological group $H$ of weight and cardinality less than or equal to the weight of $X$ such that $H$ admits a $d$-open action on $X$. This is further applied to show that if $X$ is a separable metrizable coset space of some topological group, then $X$ has a Polish extension which is a coset space of a Polish group.
