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 $(X\times\beta X)\setminus\Delta$.
@article{118648, author = {Yukinobu Yajima}, title = {Rectangular covers of products missing diagonals}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {35}, year = {1994}, pages = {147-153}, zbl = {0804.54010}, mrnumber = {1292590}, language = {en}, url = {http://dml.mathdoc.fr/item/118648} }
Yajima, Yukinobu. Rectangular covers of products missing diagonals. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 147-153. http://gdmltest.u-ga.fr/item/118648/
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