Boolean Algebra of Soft Q-Sets in Soft Topological Spaces. (28th August 2022) - Al Ghour, Samer
Abstract : 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.