### A note on topological groups and their remainders

Liang-Xue Peng, Yu-Feng He (2012)

Czechoslovak Mathematical Journal

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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 $bG$ makes the remainder and the topological group $G$ all separable and metrizable. If a non-locally compact topological group $G$ has a compactification $bG$ such that the remainder $bG\setminus G$ of $G$ belongs to $\mathcal{P}$, then $G$ and $bG\setminus G$ are separable and metrizable, where $\mathcal{P}$ is a class of spaces which satisfies the following conditions: (1) if $X\in \mathcal{P}$, then every compact subset of the...