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Countable paracompactness of Pixley-Roy hyperspaces


Author: Hidenori Tanaka
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1990-0969529-5
Keywords: Pixley-Roy hyperspace, countably paracompact, $ \Delta $-set, strong $ \Delta $-set, $ \delta $-set, almost strong $ \delta $-set, strong $ \delta $-set
Article copyright: © Copyright 1990 American Mathematical Society

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