Soft Ditopological Spaces

TL;DR

This paper introduces soft ditopological spaces, combining soft topologies and co-topologies, to generalize and study properties of spaces with both openness and closedness structures.

Contribution

It defines the concept of soft ditopological spaces, explores their basic properties, and establishes the framework for continuous mappings between them.

Findings

Defined soft ditopological spaces as soft sets with dual structures

Analyzed properties of these spaces

Established continuity concepts for mappings

Abstract

We introduce the concept of a soft ditopological space as the "soft generalization" of the concept of a ditopological space as it is defined in the papers by L.M. Brown and co-authors, see e.g. L. M. Brown, R. Erturk, S. Dost, Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems 147 (2) (2004), 17. Actually a soft ditopological space is a soft set with two independent structures on it - a soft topology and a soft co-topology. The first one is used to describe openness-type properties of a space while the second one deals with its closedness-type properties. We study basic properties of such spaces and accordingly defined continuous mappings between such spaces.