Geodesic
Almost$^*$ realcompactness
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 2, pp. 385-394.

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We provide a new generalization of realcompactness based on ultrafilters of cozero sets and contrast it with almost realcompactness.
Classification : 54D60
Keywords: almost realcompact; almost$^*$ realcompact; almost weak Oz; super countably paracompact; rc=s 
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Schommer, John J.; Swardson, Mary Anne. Almost$^*$ realcompactness. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 2, pp. 385-394. http://geodesic.mathdoc.fr/item/CMUC_2001__42_2_a15/