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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.19398 |
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Table of Contents:
- The coincidence of the $\Ind$ and $\dim$ dimensions for first countable paracompact $σ$-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.