TY - JOUR
AU - Acharyya, Sudip Kumar
AU - Bharati, Rakesh
AU - Deb Ray, Atasi
PY - 2021/10/01
Y2 - 2024/11/08
TI - Intrinsic characterizations of C-realcompact spaces
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 22
IS - 2
SE -
DO - 10.4995/agt.2021.13696
UR - https://polipapers.upv.es/index.php/AGT/article/view/13696
SP - 295-302
AB - <pre>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 thatÂ 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.</pre>
ER -