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Keywords:
Baire property; $\sigma $-compact; Čech-complete space; compactification; Čech-Stone compactification; Rajkov complete; paracompact $p$-space
Baire property; $\sigma $-compact; Čech-complete space; compactification; Čech-Stone compactification; Rajkov complete; paracompact $p$-space
Summary:
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.
References:
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