Alexander Arhangel'skii
The Baire property in remainders \break of topological groups and other results

Comment.Math.Univ.Carolinae 50,2 (2009) 273-279.

Abstract:It is established that a remainder of a non-locally compact topological group $G$ has the Baire property if and only if the space $G$ is not Čech-complete. We also show that if $G$ is a non-locally compact topological group of countable tightness, then either $G$ is submetrizable, or $G$ is the Čech-Stone remainder of an arbitrary remainder $Y$ of $G$. It follows that if $G$ and $H$ are non-submetrizable topological groups of countable tightness such that some remainders of $G$ and $H$ are homeomorphic, then the spaces $G$ and $H$ are homeomorphic. Some other corollaries and related results are presented.

Keywords: Baire property, $\sigma $-compact, Čech-complete space, compactification, Čech-Stone compactification, Rajkov complete, paracompact $p$-space
AMS Subject Classification: 54H11 54H15 54B05

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