| In this paper we show that a quasi--$G^*_{delta}$--diagonal plays a central role in metrizability. <p> We prove that: if $X$ is a first--countable $GO$--space, then $X$ is metrizable if and only if $X$ is quasi--$sigma$--space; a $wtheta$--space is metrizable if and only if it is a quasi--Nagata space with a quasi--$G^*_{delta}(2)$--diagonal; a linearly ordered space $X$ with a quasi--$G^*_{delta}(2)$--diagonal is a $Theta$--space; a space $X$ is developable if and only if it is a $wtheta$, $beta$--space with a quasi--$G^*_{delta}(2)$--diagonal. |
Keywords
$theta$--space; $Theta$--space; quasi--$sigma$--space; metrizable; quasi--$G_{delta}$-diagonal; quasi--$G^*_{delta}$-diagonal.
Math Review Classification
Primary 54E30, 54E35
Last Updated
Length
10 pages
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