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arXiv · 2410.19398

On a Problem of Arkhangel'skii

I. M. Leibo
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Abstract

The coincidence of the $\Ind$ and $\dim$ dimensions for first countable paracompact $\sigma$-spaces is proved. As a corollary, the equality $\Ind X= \dim X$ for every Nagata (that is, first countable stratifiable) space $X$ is obtained. This gives a positive answer to A.~V.~Ar\-khan\-gel'\-skii's question of whether the dimensions $\ind$, $\Ind$, and $\dim$ coincide for first countable spaces with a countable network.

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I. M. Leibo. 2024-10-25. On a Problem of Arkhangel'skii. https://arxiv.org/abs/2410.19398

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