Some classes of topological spaces related to zero-sets
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 pr...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2022-04-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/15668 |
| _version_ | 1818307186380505088 |
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| author | F. Golrizkhatami Ali Taherifar |
| author_facet | F. Golrizkhatami Ali Taherifar |
| author_sort | F. Golrizkhatami |
| collection | DOAJ |
| description | 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#-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, clTZ 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. |
| first_indexed | 2024-12-13T06:54:22Z |
| format | Article |
| id | doaj.art-0475bf0b0a034f6383b11164b41e6129 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-13T06:54:22Z |
| publishDate | 2022-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-0475bf0b0a034f6383b11164b41e61292022-12-21T23:56:04ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472022-04-0123111610.4995/agt.2022.1566813090Some classes of topological spaces related to zero-setsF. Golrizkhatami0Ali Taherifar1Yasouj University, IranYasouj University, IranAn 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#-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, clTZ 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.https://polipapers.upv.es/index.php/AGT/article/view/15668zero-setalmost p-spacecompact spacez-embedded subset |
| spellingShingle | F. Golrizkhatami Ali Taherifar Some classes of topological spaces related to zero-sets Applied General Topology zero-set almost p-space compact space z-embedded subset |
| title | Some classes of topological spaces related to zero-sets |
| title_full | Some classes of topological spaces related to zero-sets |
| title_fullStr | Some classes of topological spaces related to zero-sets |
| title_full_unstemmed | Some classes of topological spaces related to zero-sets |
| title_short | Some classes of topological spaces related to zero-sets |
| title_sort | some classes of topological spaces related to zero sets |
| topic | zero-set almost p-space compact space z-embedded subset |
| url | https://polipapers.upv.es/index.php/AGT/article/view/15668 |
| work_keys_str_mv | AT fgolrizkhatami someclassesoftopologicalspacesrelatedtozerosets AT alitaherifar someclassesoftopologicalspacesrelatedtozerosets |