Countable paracompactness of Pixley-Roy hyperspaces
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- by Hidenori Tanaka
- Proc. Amer. Math. Soc. 108 (1990), 1115-1120
- DOI: https://doi.org/10.1090/S0002-9939-1990-0969529-5
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Abstract:
In this paper, for the Pixley-Roy hyperspace $\mathcal {\mathcal {F}}[M]$ of a separable metric space $M$, it will be shown that $\mathcal {F}[M]$ is countably paracompact if and only if $\mathcal {F}{[M]^n}$ is countably paracompact for each $n \in N$ if and only if $M$ is a strong $\Delta$-set. This gives an affirmative answer to D. J. Lutzer’s problem.References
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Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 1115-1120
- MSC: Primary 54B20; Secondary 54D18, 54E30, 54E35
- DOI: https://doi.org/10.1090/S0002-9939-1990-0969529-5
- MathSciNet review: 969529