New topologies derived from the old one via operators
The main purpose of this work is to study the ideal topology defined by the minimal and maximal ideals on a topological space. Also, we define and investigate the concepts of ideal quotient and annihilator of any subfamily of 2X{2}^{X}, where 2X{2}^{X} is the power set of XX. We obtain some of their...
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| Language: | English |
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De Gruyter
2025-04-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2024-0094 |
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| author | Issaka Faical Yacine Özkoç Murad |
| author_facet | Issaka Faical Yacine Özkoç Murad |
| author_sort | Issaka Faical Yacine |
| collection | DOAJ |
| description | The main purpose of this work is to study the ideal topology defined by the minimal and maximal ideals on a topological space. Also, we define and investigate the concepts of ideal quotient and annihilator of any subfamily of 2X{2}^{X}, where 2X{2}^{X} is the power set of XX. We obtain some of their fundamental properties. In addition, several relationships among the above notions have been discussed. Moreover, we define a new topology on an ideal topological space, called sharp topology, via the sharp operator defined in this study, which turns out to be finer than the original topology. Furthermore, a decomposition of open sets (in the original topology) has been obtained. Finally, we conclude our work with some interesting applications. |
| format | Article |
| id | doaj-art-7a9a5b47f6c24cb2a8cd1febb68360ff |
| institution | OA Journals |
| issn | 2391-4661 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj-art-7a9a5b47f6c24cb2a8cd1febb68360ff2025-08-20T02:17:13ZengDe GruyterDemonstratio Mathematica2391-46612025-04-0158186387410.1515/dema-2024-0094New topologies derived from the old one via operatorsIssaka Faical Yacine0Özkoç Murad1Mathematics, Graduate School of Natural and Applied Sciences, Muğla Sıtkı Koçman University, 48000, Menteşe-Muğla, TurkeyDepartment of Mathematics, Faculty of Science, Muğla Sıtkı Koçman University, 48000, Menteşe-Muğla, TurkeyThe main purpose of this work is to study the ideal topology defined by the minimal and maximal ideals on a topological space. Also, we define and investigate the concepts of ideal quotient and annihilator of any subfamily of 2X{2}^{X}, where 2X{2}^{X} is the power set of XX. We obtain some of their fundamental properties. In addition, several relationships among the above notions have been discussed. Moreover, we define a new topology on an ideal topological space, called sharp topology, via the sharp operator defined in this study, which turns out to be finer than the original topology. Furthermore, a decomposition of open sets (in the original topology) has been obtained. Finally, we conclude our work with some interesting applications.https://doi.org/10.1515/dema-2024-0094maximal idealminimal idealideal quotientannihilatorsharp-operatorsharp-topology54a1054c6047h04 |
| spellingShingle | Issaka Faical Yacine Özkoç Murad New topologies derived from the old one via operators Demonstratio Mathematica maximal ideal minimal ideal ideal quotient annihilator sharp-operator sharp-topology 54a10 54c60 47h04 |
| title | New topologies derived from the old one via operators |
| title_full | New topologies derived from the old one via operators |
| title_fullStr | New topologies derived from the old one via operators |
| title_full_unstemmed | New topologies derived from the old one via operators |
| title_short | New topologies derived from the old one via operators |
| title_sort | new topologies derived from the old one via operators |
| topic | maximal ideal minimal ideal ideal quotient annihilator sharp-operator sharp-topology 54a10 54c60 47h04 |
| url | https://doi.org/10.1515/dema-2024-0094 |
| work_keys_str_mv | AT issakafaicalyacine newtopologiesderivedfromtheoldoneviaoperators AT ozkocmurad newtopologiesderivedfromtheoldoneviaoperators |