On the closure of one point sets in \(T_0\)-spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909934860369920 |
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| author | Dovgoshey, Oleksiy Shanin, Ruslan |
| author_facet | Dovgoshey, Oleksiy Shanin, Ruslan |
| contents | Let $X$ be a set and $2^X$ be a set of all subsets of $X$. The necessary and sufficient conditions under which a mapping $X \to 2^X$ is a closure of one-point sets in some $T_0$-space $(X, τ)$ are described. It is proved that every $T_0$-Alexandroff space is quasi-metrizable by some equidistant quasi-metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00865 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the closure of one point sets in \(T_0\)-spaces Dovgoshey, Oleksiy Shanin, Ruslan General Topology 54A10, 54D10 Let $X$ be a set and $2^X$ be a set of all subsets of $X$. The necessary and sufficient conditions under which a mapping $X \to 2^X$ is a closure of one-point sets in some $T_0$-space $(X, τ)$ are described. It is proved that every $T_0$-Alexandroff space is quasi-metrizable by some equidistant quasi-metric. |
| title | On the closure of one point sets in \(T_0\)-spaces |
| topic | General Topology 54A10, 54D10 |
| url | https://arxiv.org/abs/2512.00865 |