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Paracompactness of Pixley-Roy hyperspaces. I


Author: Hidenori Tanaka
Journal: Proc. Amer. Math. Soc. 85 (1982), 108-112
MSC: Primary 54B20; Secondary 54D18, 54F05
DOI: https://doi.org/10.1090/S0002-9939-1982-0647909-0
MathSciNet review: 647909
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Abstract: In this paper, we will study the relations between the paracompactness of a Pixley-Roy hyperspace $ \mathcal{F}\left[ X \right]$ and the paracompactness of the subspace $ {\mathcal{F}_2}\left[ X \right]$. We will give the affirmative answer to H. Bennett's problem.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0647909-0
Keywords: Paracompact, Pixley-Roy hyperspace, linearly ordered topological space, generalized ordered space, collectionwise Hausdorff, weakly separated
Article copyright: © Copyright 1982 American Mathematical Society

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