Which topologies are quasimetrizable?

AbstractA characterization of quasimetrizable spaces is given; they are those whose topologies arise from a σ-self-cocushioned pairbase whose dual is σ-self-cocushioned.This is closely related to the known characterization of γ-spaces as those whose topologies arise from a σ-self-cocushioned pairbase (with no dual condition).The last section of the paper discusses to what extent this is a topological characterization of quasimetrizability, and notes the absence of a “Bing-style” characterization