Abstract: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.
Keywords: regular $F_{\sigma}$-subsets, almost realcompactness, almost* realcompactness, r-weak cb, regular Oz, regular countably paracompact
AMS Subject Classification: 54D60