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Keywords:
$\Sigma$-space; $G_\delta$-diagonal; $\sigma$-closure-preserving; $\sigma$-cushioned; rectangular cover; \newline orthocompact; metacompact; Fréchet space
$\Sigma$-space; $G_\delta$-diagonal; $\sigma$-closure-preserving; $\sigma$-cushioned; rectangular cover; \newline orthocompact; metacompact; Fréchet space
Summary:
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 $(X\times\beta X)\setminus\Delta$.
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