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A note on topological groups and their remainders

Liang-Xue Peng; Yu-Feng He — 2012

Czechoslovak Mathematical Journal

In this note we first give a summary that on property of a remainder of a non-locally compact topological group $G$ in a compactification $b G$ makes the remainder and the topological group $G$ all separable and metrizable. If a non-locally compact topological group $G$ has a compactification $b G$ such that the remainder $b G ∖ G$ of $G$ belongs to $𝒫$ , then $G$ and $b G ∖ G$ are separable and metrizable, where $𝒫$ is a class of spaces which satisfies the following conditions: (1) if $X \in 𝒫$ , then every compact subset of the space $X$ is a...

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