On the closure of one point sets in T0-spaces
: Dovgoshey, Oleksiy; Shanin, Ruslan
Publisher: Elsevier BV
: 2026
Topology and its Applications
: 109756
: 382
: 0166-8641
: 1879-3207
DOI: https://doi.org/10.1016/j.topol.2026.109756
: https://doi.org/10.1016/j.topol.2026.109756
: https://research.utu.fi/converis/portal/detail/Publication/515570412
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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Oleksiy Dovgoshey was supported by grant 359772 of the Academy of Finland. Open access supported by Turku University.
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