A note on identifications of metric spaces

Siwiec, Frank

doi:10.1090/S0002-9939-1976-0413053-8

A note on identifications of metric spaces
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Proc. Amer. Math. Soc. 57 (1976), 340-344 Request permission

Abstract:

A space $X$ is said to be $\sigma MK$ provided that $X$ has a countable closed cover $\mathcal {C}$ of metrizable subspaces such that if $K$ is a compact subset of $X$, there is a $C \in \mathcal {C}$ for which $K \subset C$. A Hausdorff space is $\sigma MK$ and Fréchet if and only if it is representable as a closed image of a metric space obtained by identifying a discrete collection of closed sets with hemicompact boundaries to points.

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