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The Paranormality of Products and Their Subsets

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Abstract

A topological space is called paranormal if any countable discrete system of closed sets {Dn:n = 1, 2, 3,...} can be expanded to a locally finite system of open sets {Un:n = 1, 2, 3,...}, i.e., Dn is contained in Un for all n, and Dm ∩ Un≠ Ø if and only if Dm = Dn. It is proved that if X is a countably compact space whose cube is hereditarily paranormal, then X is metrizable.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    A. V. Bogomolov

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  1. A. V. Bogomolov
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Correspondence to A. V. Bogomolov.

Additional information

Original Russian Text © A.V. Bogomolov, 2018, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2018, Vol. 73, No. 4, pp. 54–56.

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Bogomolov, A.V. The Paranormality of Products and Their Subsets. Moscow Univ. Math. Bull. 73, 156–157 (2018). https://doi.org/10.3103/S0027132218040058

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  • DOI: https://doi.org/10.3103/S0027132218040058

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