On the closure of one point sets in \(T₀\)-spaces

2025/11/30 by Oleksiy Dovgoshey, Dovgoshey, Oleksiy, Ruslan Shanin +1
Mathematics · #Fixed Point Theorems Analysis #Advanced Topology and Set Theory #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2512.00865

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 → 2^X is a closure of one-point sets in some T₀-space (X, τ) are described. It is proved that every T₀-Alexandroff space is quasi-metrizable by some equidistant quasi-metric.

Citations

• Hausdorff distance between ultrametric balls
• On monoids of metric preserving functions
• Pseudometric spaces. From minimality to maximality in the groups of combinatorial self-similarities
• When all Permutations are Combinatorial Similarities
• Combinatorial characterization of pseudometrics

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• Semi Lamda*-Closed Sets and New Separation Axioms in Alexandroff Spaces
• Unification approach to the separation axioms between T₀ and completely Hausdorff