On a Problem of Arkhangel'skii
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916454310346752 |
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| author | Leibo, I. M. |
| author_facet | Leibo, I. M. |
| 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_19398 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Problem of Arkhangel'skii Leibo, I. M. General Topology =54F45 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. |
| title | On a Problem of Arkhangel'skii |
| topic | General Topology =54F45 |
| url | https://arxiv.org/abs/2410.19398 |