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

Ziqin Feng

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arXiv · 1709.06879

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

Ziqin Feng

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Abstract

A space $X$ has a $\mathbb{Q}$-diagonal if $X^2\setminus \Delta$ has a $\mathcal{K}(\mathbb{Q})$-directed compact cover. We show that any compact space with a $\mathbb{Q}$-diagonal is metrizable, hence any Tychonorff space with a $\mathbb{Q}$-diagonal is cosmic. These give a positive answer to Problem 4.2 and Problem 4.8 in \cite{COT11} raised by Cascales, Orihuela and Tkachuk.

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Ziqin Feng. 2017-09-20. Spaces with a $\mathbb{Q}$-diagonal. https://arxiv.org/abs/1709.06879

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