On the closure of one point sets in $T_0$-spaces

Oleksiy Dovgoshey; Ruslan Shanin

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arXiv · 2512.00865

On the closure of one point sets in $T_0$-spaces

Oleksiy Dovgoshey·Ruslan Shanin

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Abstract

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 $(X, \tau)$ are described. It is proved that every $T_0$-Alexandroff space is quasi-metrizable by some equidistant quasi-metric.

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BibTeX RIS

Oleksiy Dovgoshey, Ruslan Shanin. 2025-11-30. On the closure of one point sets in $T_0$-spaces. https://arxiv.org/abs/2512.00865

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