On pre Open Regular Spaces
In this paper, certain types of regularity of topological spaces have been highlighted, which fall within the study of generalizations of separation axioms. One of the important axioms of separation is what is called regularity, and the spaces that have this property are not few, and the most impor...
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University of Baghdad, College of Science for Women
2024-12-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/9237 |
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| author | Afraa R. Sadek |
| author_facet | Afraa R. Sadek |
| author_sort | Afraa R. Sadek |
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In this paper, certain types of regularity of topological spaces have been highlighted, which fall within the study of generalizations of separation axioms. One of the important axioms of separation is what is called regularity, and the spaces that have this property are not few, and the most important of these spaces are Euclidean spaces. Therefore, limiting this important concept to topology is within a narrow framework, which necessitates the use of generalized open sets to obtain more good characteristics and preserve the properties achieved in general topology. Perhaps the reader will realize through the research that our generalization preserved most of the characteristics, the most important of which is the hereditary property. Two types of regular spaces have been presented, namely the topological space Rp and the topological space S-Rp. The properties of these two spaces and their relationship with each other, as well as the effect of functions on them, have been studied. In addition several theorems have been proved regarding the sufficient and necessary conditions to make the topological spaces Rp-regular or S-Rp-regular. The above concepts have been linked with a new type of Hausdorff space and the concepts under study are reinforced with examples.
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| format | Article |
| id | doaj-art-523f1711b21c46ad890ca1e80a1a07bc |
| institution | Matheson Library |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-523f1711b21c46ad890ca1e80a1a07bc2025-08-02T07:55:54ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862024-12-01211210.21123/bsj.2024.9237On pre Open Regular SpacesAfraa R. Sadek0https://orcid.org/0000-0002-8217-4391Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq. In this paper, certain types of regularity of topological spaces have been highlighted, which fall within the study of generalizations of separation axioms. One of the important axioms of separation is what is called regularity, and the spaces that have this property are not few, and the most important of these spaces are Euclidean spaces. Therefore, limiting this important concept to topology is within a narrow framework, which necessitates the use of generalized open sets to obtain more good characteristics and preserve the properties achieved in general topology. Perhaps the reader will realize through the research that our generalization preserved most of the characteristics, the most important of which is the hereditary property. Two types of regular spaces have been presented, namely the topological space Rp and the topological space S-Rp. The properties of these two spaces and their relationship with each other, as well as the effect of functions on them, have been studied. In addition several theorems have been proved regarding the sufficient and necessary conditions to make the topological spaces Rp-regular or S-Rp-regular. The above concepts have been linked with a new type of Hausdorff space and the concepts under study are reinforced with examples. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/9237Preopen set, Pre closed set, Pre open function, Pre continuous function, Pre-irresolute map, Regular space |
| spellingShingle | Afraa R. Sadek On pre Open Regular Spaces مجلة بغداد للعلوم Preopen set, Pre closed set, Pre open function, Pre continuous function, Pre-irresolute map, Regular space |
| title | On pre Open Regular Spaces |
| title_full | On pre Open Regular Spaces |
| title_fullStr | On pre Open Regular Spaces |
| title_full_unstemmed | On pre Open Regular Spaces |
| title_short | On pre Open Regular Spaces |
| title_sort | on pre open regular spaces |
| topic | Preopen set, Pre closed set, Pre open function, Pre continuous function, Pre-irresolute map, Regular space |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/9237 |
| work_keys_str_mv | AT afraarsadek onpreopenregularspaces |