Maximal Soft Compact and Maximal Soft Connected Topologies
In various articles, it is said that the class of all soft topologies on a common universe forms a complete lattice, but in this paper, we prove that it is a complete lattice. Some soft topologies are maximal, and some are minimal with respect to specific soft topological properties. We study the pr...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Applied Computational Intelligence and Soft Computing |
| Online Access: | http://dx.doi.org/10.1155/2022/9860015 |
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| _version_ | 1832548393238396928 |
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| author | Samer Al Ghour Zanyar A. Ameen |
| author_facet | Samer Al Ghour Zanyar A. Ameen |
| author_sort | Samer Al Ghour |
| collection | DOAJ |
| description | In various articles, it is said that the class of all soft topologies on a common universe forms a complete lattice, but in this paper, we prove that it is a complete lattice. Some soft topologies are maximal, and some are minimal with respect to specific soft topological properties. We study the properties of soft compact and soft connected topologies that are maximal. Particularly, we prove that a maximal soft compact topology has identical families of soft compact and soft closed sets. We further show that a maximal soft compact topology is soft T1, while a maximal soft connected topology is soft T0. Lastly, we establish that each soft connected relative topology to a maximal soft connected topology is maximal. |
| format | Article |
| id | doaj-art-5067254ec1f545c7bd10b0750374e887 |
| institution | Kabale University |
| issn | 1687-9732 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Applied Computational Intelligence and Soft Computing |
| spelling | doaj-art-5067254ec1f545c7bd10b0750374e8872025-02-03T06:14:11ZengWileyApplied Computational Intelligence and Soft Computing1687-97322022-01-01202210.1155/2022/9860015Maximal Soft Compact and Maximal Soft Connected TopologiesSamer Al Ghour0Zanyar A. Ameen1Department of Mathematics and StatisticsDepartment of MathematicsIn various articles, it is said that the class of all soft topologies on a common universe forms a complete lattice, but in this paper, we prove that it is a complete lattice. Some soft topologies are maximal, and some are minimal with respect to specific soft topological properties. We study the properties of soft compact and soft connected topologies that are maximal. Particularly, we prove that a maximal soft compact topology has identical families of soft compact and soft closed sets. We further show that a maximal soft compact topology is soft T1, while a maximal soft connected topology is soft T0. Lastly, we establish that each soft connected relative topology to a maximal soft connected topology is maximal.http://dx.doi.org/10.1155/2022/9860015 |
| spellingShingle | Samer Al Ghour Zanyar A. Ameen Maximal Soft Compact and Maximal Soft Connected Topologies Applied Computational Intelligence and Soft Computing |
| title | Maximal Soft Compact and Maximal Soft Connected Topologies |
| title_full | Maximal Soft Compact and Maximal Soft Connected Topologies |
| title_fullStr | Maximal Soft Compact and Maximal Soft Connected Topologies |
| title_full_unstemmed | Maximal Soft Compact and Maximal Soft Connected Topologies |
| title_short | Maximal Soft Compact and Maximal Soft Connected Topologies |
| title_sort | maximal soft compact and maximal soft connected topologies |
| url | http://dx.doi.org/10.1155/2022/9860015 |
| work_keys_str_mv | AT sameralghour maximalsoftcompactandmaximalsoftconnectedtopologies AT zanyaraameen maximalsoftcompactandmaximalsoftconnectedtopologies |