@article{Golrizkhatami_Taherifar_2022, title={Some classes of topological spaces related to zero-sets}, volume={23}, url={https://ojs.upv.es/index.php/AGT/article/view/15668}, DOI={10.4995/agt.2022.15668}, abstractNote={<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>}, number={1}, journal={Applied General Topology}, author={Golrizkhatami, F. and Taherifar, Ali}, year={2022}, month={Apr.}, pages={1–16} }