Countable paracompactness of Pixley-Roy hyperspaces

Tanaka, Hidenori

doi:10.1090/S0002-9939-1990-0969529-5

Countable paracompactness of Pixley-Roy hyperspaces
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Proc. Amer. Math. Soc. 108 (1990), 1115-1120 Request permission

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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