Closed mappings of 𝜎-locally compact metric spaces

Stricklen, S. A.

doi:10.1090/S0002-9939-1975-0377805-4

Closed mappings of $\sigma$-locally compact metric spaces
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Proc. Amer. Math. Soc. 51 (1975), 221-224 Request permission

Abstract:

We show that a metric space $M$ is $\sigma$-locally compact if and only if every image of $M$ under a closed, continuous function is the countable union of closed, metrizable, locally compact subspaces. Several other theorems about closed, continuous images of metric spaces are given; one of these is that the closed, continuous image of a complete, $\sigma$-locally compact metric space must contain a dense, metrizable open set.

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