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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Closed mappings of $ \sigma $-locally compact metric spaces

Author: S. A. Stricklen
Journal: Proc. Amer. Math. Soc. 51 (1975), 221-224
MSC: Primary 54C10
MathSciNet review: 0377805
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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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Keywords: Closed, continuous images of metric spaces, upper semicontinuous decompositions of metric spaces, countable union of closed, metrizable subspaces
Article copyright: © Copyright 1975 American Mathematical Society