Soft Somewhat Continuous and Soft Somewhat Open Functions

TL;DR

This paper introduces and studies the properties of soft somewhat open sets and functions within soft topology, including continuity, openness, homeomorphisms, and topological invariants, with multiple illustrative examples.

Contribution

It defines soft somewhat open sets and functions, explores their properties, and characterizes soft somewhat continuous and open functions, advancing soft topological theory.

Findings

Soft somewhat open sets are contained in soft somewhere dense sets.

Characterizations of soft somewhat continuous and open functions are provided.

Topological invariants for soft somewhat homeomorphisms are discussed.

Abstract

In this paper, we define a soft somewhat open set using the soft interior operator. We study main properties the class of soft somewhat open sets that is contained in the class soft somewhere dense sets. Then, we introduce the classes of soft somewhat continuous and soft somewhat open functions and soft somewhat homeomorphisms. Moreover, we study properties and characterizations of soft somewhat continuous and soft somewhat open functions. At last, we discuss topological invariants for soft somewhat homeomorphisms. Multiple examples are offered to clarify some invalid results.