A novel approach to study soft preopen sets inspired by classical topologies

Abstract

Our target in the present work, is presenting the idea of weakly soft preopen (ws-preopen) subsets and studying some of its characterizations. With the assistance of some elucidative examples, the interrelationships between ws-preopen sets and some extensions of soft open sets are studied. Under some conditions such as extended and hyperconnected soft topologies, several motivating results and relationships are acquired. The interior and closure operators that built through ws-preopen and ws-preclosed subsets are introduced. Their main features that construe the relations among them are established. Soft continuity with respect to theses classes of soft subsets are studied and their substantial characteristics are investigated. Generally, the systematic relations and outcomes that are lost through the scope of this study are discussed. The proposed line in the current study will present new ways to discover novel concepts in the field of soft topology.