Supra finite soft-open sets and applications to operators and continuity

Abstract

In this article, we study the concept of finite open sets in the spaces of supra soft-topologies. We aim by defining this concept to furnish the researchers with a tool they generate new forms of topological concepts via supra soft-topologies such as continuity, compactness, separation axioms, etc. We discuss the main properties of this concept and prove that this class of soft sets is neither infra soft-topology nor supra soft-topology. Also, we reveal its connections with other celebrated generalizations of supra soft-open sets and conclude the conditions they guarantee the equivalence between them. After that, we display some soft operators, like interior and closure, inspired by the classes of supra finite soft-open and supra finite soft-closed sets. Finally, we set forth some types of continuity defined by these classes and describe their main characterizations and behaviors in different cases such as decomposition theorems and transition between the realms of of supra soft-topologies and their parametric supra topologies. The obtained results and implementations are articulated with the aid of some counterexamples.