On the completeness of the space of compact subsets
Author:
Phillip Zenor
Journal:
Proc. Amer. Math. Soc. 26 (1970), 190-192
MSC:
Primary 54.20
DOI:
https://doi.org/10.1090/S0002-9939-1970-0261538-4
MathSciNet review:
0261538
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Abstract | References | Similar Articles | Additional Information
Abstract: The purpose of this paper is to show that if $X$ is a completely regular ${T_1}$-space, then $\mathcal {C}(X)$, the space of all compact subsets of $X$ with the Vietoris topology, is realcompact (topologically complete in the sense of Dieudonné) if and only if $X$ is realcompact (topologically complete in the sense of Dieudonné).
- Ernest Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152–182. MR 42109, DOI https://doi.org/10.1090/S0002-9947-1951-0042109-4
- Phillip Zenor, Extending completely regular spaces with inverse limits, Glasnik Mat. Ser. III 5(25) (1970), 157–162 (English, with Serbo-Croatian summary). MR 275371 ---, Extensions of topological spaces, (to appear).
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Additional Information
Keywords:
Hyperspace,
realcompactness,
completeness,
inverse limits
Article copyright:
© Copyright 1970
American Mathematical Society