Alexandroff–Urysohn cover metrization

Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

Palomar Registrypalomar/PALOMAR-2026-10-16-000021Oct 16, 2026math.GNscore 0

A T0 space is metrizable if and only if it admits a sequence of open covers such that every intersecting pair of members at the next level has union contained in one member at the current level, and the point-stars form a neighborhood basis. Without separation the same criterion characterizes pseudometrizability. The proof constructs a countably generated co-membership uniformity with exactly the supplied topology. Covers have unrestricted cardinality; empty spaces are included. Classical mathematics, with no novelty or priority claim.

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