Metrization and Semimetrization Theorems with Applications to Manifolds

This paper is a study of conditions under which a space with S₂ is metrizable, o-semimetrizable or semimetrizable. It is shown that: a wMN, w-space is metrizable if and only if it has S₂, a quasi--space is metrizable if and only if it is a pseudo wN-space with S₂, a separable manifold is metrizable if and only if it has S₂ with property (*), a perfectly normal manifold with q quasi-G ^* diagonal is metrizable and a separable manifold is a hereditarily separable metrizable if and only if it has -S₂.