Intrinsic characterizations of $C$-realcompact spaces
Abstract
-realcompact spaces are introduced by Karamzadeh and Keshtkar in Quaest. Math. 41(8), 2018, 1135-1167. We offer a characterization of these spaces via -stable family of closed sets in by showing that is -realcompact if and only if each -stable family of closed sets in with finite intersection property has nonempty intersection. This last condition which makes sense for an arbitrary topological space can be taken as an alternative definition of a -realcompact space. We show that each topological space can be extended as a dense subspace to a -realcompact space with some desired extension property. An allied class of spaces viz -compact spaces akin to that of -realcompact spaces are introduced. The paper ends after examining how far a known class of -realcompact spaces could be realized as -compact for appropriately chosen ideal of closed sets in .
Cite
@article{arxiv.2007.05210,
title = {Intrinsic characterizations of $C$-realcompact spaces},
author = {Sudip Kumar Acharyya and Rakesh Bharati and Atasi Deb Ray},
journal= {arXiv preprint arXiv:2007.05210},
year = {2022}
}