Geodesic
r-Realcompact spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 2, pp. 253-267.

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A new generalization of realcompactness based on ultrafilters of regular $F_{\sigma}$-subsets is introduced. Its relationship with realcompactness, almost realcompactness, almost* realcompactness, c-realcompactness is examined. Some of the properties of the newly introduced space is studied as well.
Classification : 54D60
Keywords: regular $F_{\sigma}$-subsets; almost realcompactness; almost* realcompactness; r-weak cb; regular Oz; regular countably paracompact 
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Bhattacharya, D.; Dey, Lipika. r-Realcompact spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 2, pp. 253-267. http://geodesic.mathdoc.fr/item/CMUC_2012__53_2_a6/