Strictly Wider Class of Soft Sets via Supra Soft δ-Closure Operator

Abstract

In this work, we use the supra soft δ-closure operator to present a new notion of generalized closed sets in supra soft topological spaces (or SSTSs), named supra soft δ-generalized closed sets. We show that, this notion is more general than many of previous notions, which presented before in famous papers. We illustrate many of its essential properties in detail. Specifically, we illustrate that the new collection neither forms soft topology nor supra soft topology. Moreover, we study the behavior of the soft image and soft pre-images of supra soft δ-generalized closed sets under new types of soft mappings, named supra soft irresolute and supra soft δ-irresolute closed. In addition, we define the concept of supra soft δ-generalized open sets, as a complement of supra soft δ-generalized closed sets. Finally, the relationships with other forms of generalized open sets in SSTSs are explored, supported by concrete examples and counterexamples. Therefore, I think the development of the notions presented in this paper are sufficiently general relevance to allow for future extensions.