Intrinsic characterizations of C-realcompact spaces
| Autor: | Sudip Kumar Acharyya, Rakesh Bharati, Atasi Deb Ray |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Applied General Topology, Vol 22, Iss 2, Pp 295-302 (2021) |
| Druh dokumentu: | article |
| ISSN: | 1576-9402 1989-4147 |
| DOI: | 10.4995/agt.2021.13696 |
| Popis: | c-realcompact spaces are introduced by Karamzadeh and Keshtkar in Quaest. Math. 41, no. 8 (2018), 1135-1167. We offer a characterization of these spaces X via c-stable family of closed sets in X by showing that X is c-realcompact if and only if each c-stable family of closed sets in X 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 c-realcompact space. We show that each topological space can be extended as a dense subspace to a c-realcompact space with some desired extension properties. An allied class of spaces viz CP-compact spaces akin to that of c-realcompact spaces are introduced. The paper ends after examining how far a known class of c-realcompact spaces could be realized as CP-compact for appropriately chosen ideal P of closed sets in X. |
| Databáze: | Directory of Open Access Journals |
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