An alternative to Bing's generalization of Urysohn's metrization theorem

Abstract

We show that the General Metrization Problem posed by the advent of Urysohn's Theorem has solutions other than those in Bing's Theorem and its generalizations, and give a theorem that uses no counterpart to Bing's discreteness or (any of its generalizations such as) local finiteness or the closure preserving property or the cushion property. There, metrizability is equated to some sort of Regularity, with the separating open sets (of a closed set and a point) coming in in a specific manner from a specific family.