Soft Maximal Topologies

TL;DR

This paper investigates the lattice structure of soft topologies, proving it forms a complete lattice, and explores properties of maximal soft compact and soft connected topologies, including their compactness, connectedness, and separation properties.

Contribution

It establishes that the class of all soft topologies on a common universe forms a complete lattice and analyzes properties of maximal soft compact and connected topologies.

Findings

The class of all soft topologies forms a complete lattice.

Maximal soft compact topologies have identical families of soft compact and soft closed sets.

Maximal soft compact topologies are soft T1.

Abstract

In various articles, it is said that the class of all soft topologies on a common universe forms a complete lattice, but in this paper, we prove that it is a complete lattice. Some soft topologies are maximal and some are minimal with respect to certain soft topological properties. We study the properties of soft compact and soft connected topologies that are maximal. In particular, we prove that a maximal soft compact topology has identical families of soft compact and soft closed sets, and it is also soft $T_1$.