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Proceedings of the American Mathematical Society

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

 
 

 

A note on identifications of metric spaces


Author: Frank Siwiec
Journal: Proc. Amer. Math. Soc. 57 (1976), 340-344
MSC: Primary 54E20; Secondary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1976-0413053-8
MathSciNet review: 0413053
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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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DOI: https://doi.org/10.1090/S0002-9939-1976-0413053-8
Keywords: $ \sigma MK$ space, closed image of a metric space
Article copyright: © Copyright 1976 American Mathematical Society

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