g_*^*-I-Closed Sets and Their Properties in in Ideal Topological Space
There are many research papers that deal with different types of generalized closed sets. Levine [4] introduced generalized closed (briefly, -closed) sets and studied their basic properties and Veera Kumar [5] introduced -closed sets in topological spaces. The purpose of this present paper is to def...
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| Format: | Article |
| Language: | Arabic |
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College of Computer Science and Mathematics, University of Mosul
2025-05-01
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| Series: | المجلة العراقية للعلوم الاحصائية |
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| Online Access: | https://stats.uomosul.edu.iq/article_187753_e0d33f3d948a5941a79bf987e1eaf1a3.pdf |
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| _version_ | 1850164101350686720 |
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| author | Rughzai Mahamood Darwesh Mohammed |
| author_facet | Rughzai Mahamood Darwesh Mohammed |
| author_sort | Rughzai Mahamood |
| collection | DOAJ |
| description | There are many research papers that deal with different types of generalized closed sets. Levine [4] introduced generalized closed (briefly, -closed) sets and studied their basic properties and Veera Kumar [5] introduced -closed sets in topological spaces. The purpose of this present paper is to define a new class of generalized idea closed sets called -closed sets by using -open set .In this paper, we introduce the -closed sets, characterizations and properties of -closed sets and its complement and other related sets. We prove that the class of closed sets lies between the class of -closed sets and the class of -closed sets. Also, we find some relations between -closed sets and already existing closed sets. -open neighborhood is introduced and their properties are investigated. |
| format | Article |
| id | doaj-art-aa4af262d35c4a5cbc58dd8b2bb3db65 |
| institution | OA Journals |
| issn | 1680-855X 2664-2956 |
| language | Arabic |
| publishDate | 2025-05-01 |
| publisher | College of Computer Science and Mathematics, University of Mosul |
| record_format | Article |
| series | المجلة العراقية للعلوم الاحصائية |
| spelling | doaj-art-aa4af262d35c4a5cbc58dd8b2bb3db652025-08-20T02:22:04ZaraCollege of Computer Science and Mathematics, University of Mosulالمجلة العراقية للعلوم الاحصائية1680-855X2664-29562025-05-01221394610.33899/iqjoss.2025.187753187753g_*^*-I-Closed Sets and Their Properties in in Ideal Topological SpaceRughzai Mahamood0Darwesh Mohammed1Department of Mathematics, College of Science, University of Sulaimani, Sulaimani, IraqDepartment of Mathematics, College of Science, University of Sulaimani, Sulaimani, IraqThere are many research papers that deal with different types of generalized closed sets. Levine [4] introduced generalized closed (briefly, -closed) sets and studied their basic properties and Veera Kumar [5] introduced -closed sets in topological spaces. The purpose of this present paper is to define a new class of generalized idea closed sets called -closed sets by using -open set .In this paper, we introduce the -closed sets, characterizations and properties of -closed sets and its complement and other related sets. We prove that the class of closed sets lies between the class of -closed sets and the class of -closed sets. Also, we find some relations between -closed sets and already existing closed sets. -open neighborhood is introduced and their properties are investigated.https://stats.uomosul.edu.iq/article_187753_e0d33f3d948a5941a79bf987e1eaf1a3.pdfideal topological spaceg^*-closed setg^*-i-closed setg_*^*-i-open set |
| spellingShingle | Rughzai Mahamood Darwesh Mohammed g_*^*-I-Closed Sets and Their Properties in in Ideal Topological Space المجلة العراقية للعلوم الاحصائية ideal topological space g^*-closed set g^*-i-closed set g_*^*-i-open set |
| title | g_*^*-I-Closed Sets and Their Properties in in Ideal Topological Space |
| title_full | g_*^*-I-Closed Sets and Their Properties in in Ideal Topological Space |
| title_fullStr | g_*^*-I-Closed Sets and Their Properties in in Ideal Topological Space |
| title_full_unstemmed | g_*^*-I-Closed Sets and Their Properties in in Ideal Topological Space |
| title_short | g_*^*-I-Closed Sets and Their Properties in in Ideal Topological Space |
| title_sort | g i closed sets and their properties in in ideal topological space |
| topic | ideal topological space g^*-closed set g^*-i-closed set g_*^*-i-open set |
| url | https://stats.uomosul.edu.iq/article_187753_e0d33f3d948a5941a79bf987e1eaf1a3.pdf |
| work_keys_str_mv | AT rughzaimahamood giclosedsetsandtheirpropertiesininidealtopologicalspace AT darweshmohammed giclosedsetsandtheirpropertiesininidealtopologicalspace |