Application of ic—open Sets in Topologies Via Ideals
In this paper, new kinds of open sets inside ideal topological spaces are introduced; they are called ic - I - open,icc - I -open,weakly ic - I - open and weakly icc - I - open. Some properties and relations between these new classes are studied with examples. The concept of continuity in ideal topo...
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| Language: | English |
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Mosul University
2024-06-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
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| Online Access: | https://csmj.mosuljournals.com/article_183926_6a8c54983f3b4968f63904fc22e2a638.pdf |
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| author | Rana AL -jaheishi Amir AL- siraj |
| author_facet | Rana AL -jaheishi Amir AL- siraj |
| author_sort | Rana AL -jaheishi |
| collection | DOAJ |
| description | In this paper, new kinds of open sets inside ideal topological spaces are introduced; they are called ic - I - open,icc - I -open,weakly ic - I - open and weakly icc - I - open. Some properties and relations between these new classes are studied with examples. The concept of continuity in ideal topological spaces is also presented for these new classes. Theorems that provide an equivalence relation between these new classes are proved. Also, for ideal topological spaces (Ɲ, Ʈ, I) we show that all open sets are ic -I- open, icc - I - open, weakly ic - I - open, weakly icc - I - open . Finally, Assume Z ⊂ Ɲ of ideal Topological spaces (Ɲ,Ʈ,l ). Then 1) if Z is semi - I - open, then Zc is ic – I - open.2) if Z is open and ic - I - closed, then Z is semi - I - open. |
| format | Article |
| id | doaj-art-058cc95f55b5457fb3cd329ecdc82ca7 |
| institution | OA Journals |
| issn | 1815-4816 2311-7990 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Mosul University |
| record_format | Article |
| series | Al-Rafidain Journal of Computer Sciences and Mathematics |
| spelling | doaj-art-058cc95f55b5457fb3cd329ecdc82ca72025-08-20T01:59:30ZengMosul UniversityAl-Rafidain Journal of Computer Sciences and Mathematics1815-48162311-79902024-06-01181929510.33899/csmj.2024.146288.1104183926Application of ic—open Sets in Topologies Via IdealsRana AL -jaheishi0Amir AL- siraj1Department of Mathematics, College of Education for Pure Sciences, University of Mosul, IraqDepartment of Mathematics, College of Education for Pure Sciences, University of Mosul, IraqIn this paper, new kinds of open sets inside ideal topological spaces are introduced; they are called ic - I - open,icc - I -open,weakly ic - I - open and weakly icc - I - open. Some properties and relations between these new classes are studied with examples. The concept of continuity in ideal topological spaces is also presented for these new classes. Theorems that provide an equivalence relation between these new classes are proved. Also, for ideal topological spaces (Ɲ, Ʈ, I) we show that all open sets are ic -I- open, icc - I - open, weakly ic - I - open, weakly icc - I - open . Finally, Assume Z ⊂ Ɲ of ideal Topological spaces (Ɲ,Ʈ,l ). Then 1) if Z is semi - I - open, then Zc is ic – I - open.2) if Z is open and ic - I - closed, then Z is semi - I - open.https://csmj.mosuljournals.com/article_183926_6a8c54983f3b4968f63904fc22e2a638.pdfideal topological spaceic-i-openicc-i-open |
| spellingShingle | Rana AL -jaheishi Amir AL- siraj Application of ic—open Sets in Topologies Via Ideals Al-Rafidain Journal of Computer Sciences and Mathematics ideal topological space ic-i-open icc-i-open |
| title | Application of ic—open Sets in Topologies Via Ideals |
| title_full | Application of ic—open Sets in Topologies Via Ideals |
| title_fullStr | Application of ic—open Sets in Topologies Via Ideals |
| title_full_unstemmed | Application of ic—open Sets in Topologies Via Ideals |
| title_short | Application of ic—open Sets in Topologies Via Ideals |
| title_sort | application of ic open sets in topologies via ideals |
| topic | ideal topological space ic-i-open icc-i-open |
| url | https://csmj.mosuljournals.com/article_183926_6a8c54983f3b4968f63904fc22e2a638.pdf |
| work_keys_str_mv | AT ranaaljaheishi applicationoficopensetsintopologiesviaideals AT amiralsiraj applicationoficopensetsintopologiesviaideals |