| In this paper, we study Moore and semi--stratifiable spaces. We give characterizations of developable and semi--stratifiable spaces. We prove that: a regular space $X$ is semi--stratifiable if and only if it is a $beta$, quasi--semi--stratifiable and the following are equivalent for a regular $wDelta$--space $X$: begin{enumerate} item[(a)] $X$ is a Moore space; item[(b)] $X$ is a hereditarily weakly $theta$--refinable space with a quasi--${G}_delta$--diagonal; item[(c)] $X$ is a quasi--${G}^{*}_delta$--diagonal; item[(d)] $X$ is a quasi--semi--stratifiable space; item[(e)] $X$ is a quasi--$alpha$--space. end{enumerate} |
Keywords
semi--stratifiable space; weakly $gamma$--space; weakly $beta$--space; metrizable; Moore space; quasi--$alpha$--space; quasi--$G^*_{delta}$--diagonal.
Math Review Classification
Primary 54E30, 54E35
Last Updated
Length
6 pages
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