Geodesic
The Baire property in remainders of topological groups and other results
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 2, pp. 273-279 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 54B05, 54H11, 54H15
Keywords: Baire property; $\sigma $-compact; Čech-complete space; compactification; Čech-Stone compactification; Rajkov complete; paracompact $p$-space 
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     author = {Arhangel'skii, Alexander},
     title = {The {Baire} property in remainders of topological groups and other results},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {273--279},
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Arhangel'skii, Alexander. The Baire property in remainders of topological groups and other results. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 2, pp. 273-279. http://geodesic.mathdoc.fr/item/CMUC_2009_50_2_a7/