Spaces with a $\mathbb {Q}$-diagonal
Volume 245 / 2019
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).
