Factorization of Metrizability

Abstract

ABSTRACTA general method of factorization in introduced. It consists of, first, the weakening of the concept of an open base or that of a network, and, second, the restoration to the weakened concept its full vigor. Thus, every time, we have the restorative + the weakened concept = the original concept. The workings of the method are exceedingly simple. Its field of applications goes well beyond metrizability. Results include an improvement of Heath and Aull on the developability and metrizability of semistratifiable spaces. We also have that every Nagata space has a metrizable dense subset.