Maximal Soft Compact and Maximal Soft Connected Topologies

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 specific soft topological properties. We study the properties of soft compact and soft connected topologies that are maximal. Particularly, we prove that a maximal soft compact topology has identical families of soft compact and soft closed sets. We further show that a maximal soft compact topology is soft $T_1$ , while a maximal soft connected topology is soft $T_0$ . Lastly, we establish that each soft connected relative topology to a maximal soft connected topology is maximal.