Metrization and semimetrization theorems with applications to manifolds

Abstract

This paper is a study of conditions under which a space with S2 is metrizable, o-semimetrizable or semimetrizable. It is shown that: a wM N, wγ-space is metrizable if and only if it has S2, a quasi-γ-space is metrizable if and only if it is a pseudo wNspace with S2, a separable manifold is metrizable if and only if it has S2 with property (∗), a perfectly normal manifold with quasi-G ∗ -diagonal is metrizable and a separable