Boolean Algebra of Soft Q-Sets in Soft Topological Spaces
We define soft Q-sets as soft sets whose soft closure and soft interior are commutative. We show that the soft complement, soft closure, and soft interior of a soft Q-set are all soft Q-sets. We show that a soft subset K of a given soft topological space is a soft Q-set if and only if K is a soft sy...
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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/10.1155/2022/5200590 |
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| author | Samer Al Ghour |
| author_facet | Samer Al Ghour |
| author_sort | Samer Al Ghour |
| collection | DOAJ |
| description | We define soft Q-sets as soft sets whose soft closure and soft interior are commutative. We show that the soft complement, soft closure, and soft interior of a soft Q-set are all soft Q-sets. We show that a soft subset K of a given soft topological space is a soft Q-set if and only if K is a soft symmetric difference between a soft clopen set and a soft nowhere dense set. And as a corollary, the class of soft Q-sets contains simultaneously the classes of soft clopen sets and soft nowhere dense sets. Also, we prove that the class of soft Q-sets is closed under finite soft intersections and finite soft unions, and as a main result, we prove that the class of soft Q-sets forms a Boolean algebra. Furthermore, via soft Q-sets, we characterize soft sets whose soft boundaries and soft interiors are commutative. In addition, we investigate the correspondence between Q-sets in topological spaces and soft Q-sets in soft topological spaces. |
| format | Article |
| id | doaj-art-5c7c129f46fa4a96821c6d2ac0462235 |
| 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-5c7c129f46fa4a96821c6d2ac04622352025-02-03T05:50:39ZengWileyApplied Computational Intelligence and Soft Computing1687-97322022-01-01202210.1155/2022/5200590Boolean Algebra of Soft Q-Sets in Soft Topological SpacesSamer Al Ghour0Department of Mathematics and StatisticsWe define soft Q-sets as soft sets whose soft closure and soft interior are commutative. We show that the soft complement, soft closure, and soft interior of a soft Q-set are all soft Q-sets. We show that a soft subset K of a given soft topological space is a soft Q-set if and only if K is a soft symmetric difference between a soft clopen set and a soft nowhere dense set. And as a corollary, the class of soft Q-sets contains simultaneously the classes of soft clopen sets and soft nowhere dense sets. Also, we prove that the class of soft Q-sets is closed under finite soft intersections and finite soft unions, and as a main result, we prove that the class of soft Q-sets forms a Boolean algebra. Furthermore, via soft Q-sets, we characterize soft sets whose soft boundaries and soft interiors are commutative. In addition, we investigate the correspondence between Q-sets in topological spaces and soft Q-sets in soft topological spaces.http://dx.doi.org/10.1155/2022/5200590 |
| spellingShingle | Samer Al Ghour Boolean Algebra of Soft Q-Sets in Soft Topological Spaces Applied Computational Intelligence and Soft Computing |
| title | Boolean Algebra of Soft Q-Sets in Soft Topological Spaces |
| title_full | Boolean Algebra of Soft Q-Sets in Soft Topological Spaces |
| title_fullStr | Boolean Algebra of Soft Q-Sets in Soft Topological Spaces |
| title_full_unstemmed | Boolean Algebra of Soft Q-Sets in Soft Topological Spaces |
| title_short | Boolean Algebra of Soft Q-Sets in Soft Topological Spaces |
| title_sort | boolean algebra of soft q sets in soft topological spaces |
| url | http://dx.doi.org/10.1155/2022/5200590 |
| work_keys_str_mv | AT sameralghour booleanalgebraofsoftqsetsinsofttopologicalspaces |