TY - JOUR
AU - Golrizkhatami, F.
AU - Taherifar, Ali
PY - 2022/04/01
Y2 - 2023/12/10
TI - Some classes of topological spaces related to zero-sets
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 23
IS - 1
SE -
DO - 10.4995/agt.2022.15668
UR - https://ojs.upv.es/index.php/AGT/article/view/15668
SP - 1-16
AB - <p>An almost P-space is a topological space in which every zero-set is regular-closed. We introduce a large class of spaces, C-almost P-space (briefly CAP-space), consisting of those spaces in which the closure of the interior of every zero-set is a zero-set. In this paper we study CAP-spaces. It is proved that if X is a dense and Z<sup>#</sup>-embedded subspace of a space T, then T is CAP if and only if X is a CAP and CRZ-extended in T (i.e, for each regular-closed zero-set Z in X, cl<sub>T</sub>Z is a zero-set in T). In 6P.5 of [8] it was shown that a closed countable union of zero-sets need not be a zero-set. We call X a CZ-space whenever the closure of any countable union of zero-sets is a zero-set. This class of spaces contains the class of P-spaces, perfectly normal spaces, and is contained in the cozero complemented spaces and CAP-spaces. In this paper we study topological properties of CZ (resp. cozero complemented)-space and other classes of topological spaces near to them. Some algebraic and topological equivalent conditions of CZ (resp. cozero complemented)-space are characterized. Examples are provided to illustrate and delimit our results.</p>
ER -