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arXiv · 1711.10015

Coset spaces of metrizable groups

Sergey Antonyan·Natella Antonyan·Konstantin Kozlov
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Abstract

We characterize coset spaces of topological groups which are coset spaces of (separable) metrizable groups and complete metrizable (Polish) groups. Besides, 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 then $X$ has a Polish extension which is a coset space of a Polish group.

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Sergey Antonyan, Natella Antonyan, Konstantin Kozlov. 2017-11-27. Coset spaces of metrizable groups. https://arxiv.org/abs/1711.10015

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