Some Results on Quasi--$sigma$ and $theta$ Spaces

A.M. Mohamad


In this paper we show that a quasi--$G^*_{delta}$--diagonal
plays a central
role in metrizability.
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.

$theta$--space; $Theta$--space; quasi--$sigma$--space; metrizable; quasi--$G_{delta}$-diagonal; quasi--$G^*_{delta}$-diagonal.

Math Review Classification
Primary 54E30, 54E35

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10 pages

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