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Spaces with a $\mathbb {Q}$-diagonal

Volume 245 / 2019

Ziqin Feng Fundamenta Mathematicae 245 (2019), 305-320 MSC: Primary 54E35; Secondary 54B10, 54D30. DOI: 10.4064/fm615-8-2018 Published online: 1 February 2019

Abstract

A space $X$ has a $\mathbb {Q}$-diagonal if $X^2\setminus \varDelta $ has a $\mathcal {K}(\mathbb {Q})$-directed compact cover. We show that any compact space with a $\mathbb {Q}$-diagonal is metrizable, hence any Tikhonov space with a $\mathbb {Q}$-diagonal is cosmic. This gives positive answers to two problems by Cascales, Orihuela, and Tkachuk (2011).

Authors

  • Ziqin FengDepartment of Mathematics and Statistics
    Auburn University
    Auburn, AL 36849, U.S.A.
    e-mail

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