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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1687-9732 |