Determinations of soft topologies

Abstract

Cryptomorphic properties of soft topologies are studied in this paper. For an arbitrary set X, appropriate order relations ≤ on SWℂL(X, I) (the set of all soft weak closure operators on X indexed by I), SWIℕ(X, I) (the set of all soft weak interior operators on X indexed by I), SWOU(X, I) (the set of all soft weak exterior operators on X indexed by I), and SWB(X, I) (the set of all soft weak boundary operators on X indexed by I) are defined respectively, which make (SWℂL(X, I),≤), (SWIN(X, I),≤), (SWOU(X, I),≤) and (SWB(X, I),≤) complete lattices that are isomorphic to (ST(X, I),⊆), where ST(X, I) is the set of all soft topologies on X indexed by I.