ON WEAKLY SOFT SOMEWHAT OPEN SETS

Abstract

It is well known that certain topological concepts such as the sum of topologies and the product of topologies are defined by particular classes of other topologies. In such topologies and others, it is crucial to look into the connections between these classes and the topology generated by them. One of the topologies that creates a family of general topologies is soft topology, which is defined over a family of soft sets satisfying the basic axioms of general topology. It is interesting to investigate how topological notions behave when applied to soft topologies because it enables us to study topological qualities by comparing them to their counterparts in other topologies. In this paper, we benefit from the fruitful variety via soft topology to introduce the concept of weakly soft somewhat open sets (briefly, weakly soft $so$-sets), which is constructed using its corresponding notion via parametric topologies. We demonstrate that the class of soft somewhat open sets is a stronger generalization of soft open sets than this type, and we also offer a condition that guarantees their equality. Then, we present new soft operators and discuss their essential characteristics by utilizing the notion of weakly soft $so$-sets and their complements. One of the unique characteristics that we prove of these operators is that the $so$-interior of a soft subset is the soft subset itself or the null soft set, whereas $so$-closure of a soft subset is the soft subset itself or the absolute soft set. Finally, we provide new categories of soft mappings and explore their main characteristics. We provide a few examples and counterexamples to clarify the findings and relationships obtained herein.