| In this paper, we answer two questions of P. Fletcher and W. Lindgren. We prove that a space $X$ is $wDelta$ and has a quasi--$G^*_{delta}$--diagonal if and only if it is developable, a space $X$ is $beta$--space with a quasi--$G^{*}_{delta}$--diagonal if and only if it is semi--stratifiable, a space $X$ is $beta$, quasi--$gamma$--space and has a quasi--$G^*_{delta}$--diagonal if and only if $X$ is developable and a space $X$ is metrizable if and only if it is paracompact $beta$--space with a quasi--$G_{delta}$--diagonal. |
Keywords
quasi--$wDelta$--space, quasi--developable space, quasi--$gamma$--space, $eta$--space, quasi--$G^*_{delta}$-diagonal, semi--stratifiable, $c$-semi--stratifiable.
Math Review Classification
Primary 54E30
; Secondary 54E35
Last Updated
29 September 1999
Length
7 pages
Availability
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