On the closure of one point sets in T0-spaces - UTU Research Portal

A1 Refereed original research article in a scientific journal

On the closure of one point sets in T0-spaces

Authors: Dovgoshey, Oleksiy; Shanin, Ruslan

Publisher: Elsevier BV

Publication year: 2026

Journal: Topology and its Applications

Article number: 109756

Volume: 382

ISSN: 0166-8641

eISSN: 1879-3207

DOI: https://doi.org/10.1016/j.topol.2026.109756

Publication's open availability at the time of reporting: Open Access

Publication channel's open availability : Partially Open Access publication channel

Web address : https://doi.org/10.1016/j.topol.2026.109756

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/515570412

Self-archived copy's licence: CC BY

Self-archived copy's version: Publisher`s PDF

Abstract

Let X be a set and 2X be a set of all subsets of X. The necessary and sufficient conditions under which a mapping X → 2X is a closure of one-point sets in some T0-space (X, τ) are described. It is proved that every T0-Alexandroff space is quasimetrizable by some equidistant quasi-metrics.

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Funding information in the publication:
Oleksiy Dovgoshey was supported by grant 359772 of the Academy of Finland. Open access supported by Turku University.