This paper is a study of conditions under which a space with $S_2$ is metrizable, o-semimetrizable or semimetrizable. It is shown that: a $wMN$, $wgamma$-space is metrizable if and only if it has $S_2$, a quasi-$gamma$-space is metrizable if and only if it is a pseudo $wN$-space with $S_2$, a separable manifold is metrizable if and only if it has $S_2$ with property $(*)$, a perfectly normal manifold with quasi-${G}^{*}_delta$-diagonal is metrizable and a separable manifold is a hereditarily separable metrizable if and only if it has $theta$-${alpha}_2$. |
Keywords
metrizable spaces, o-semimetrizable spaces, semimetrizable spaces and metrizable manifolds
Math Review Classification
Primary 54E30, 54E35.
Last Updated
21/4/97
Length
18 pages
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