Abstract:We give a characterization of a paracompact $\Sigma $-space to have a $G_\delta $-diagonal in terms of three rectangular covers of $X^2\setminus \Delta $. Moreover, we show that a local property and a global property of a space $X$ are given by the orthocompactness of $(X\times \beta X)\setminus \Delta $.
Keywords: $\Sigma $-space, $G_\delta $-diagonal, $\sigma $-closure-preserving, $\sigma $-cushioned, rectangular cover, \newline orthocompact, metacompact, Fr\'echet space
AMS Subject Classification: 54B10, 54D20, 54E18