Minimal Soft Topologies

Abstract

A collection of all soft topologies over a fixed universe forms a complete lattice. One might ask: what will be the structure of minimal or maximal topologies in this lattice concerning specific topological properties? We know that the soft discrete topology is maximal soft [Formula: see text]-spaces, for [Formula: see text], in terms of the given soft point theory. As a result, we find it interesting to study the construction of minimal soft [Formula: see text] topologies. We show that the minimal soft [Formula: see text] is a nested soft topology whose base is the complements of all soft point closures. The minimal soft [Formula: see text] is the cofinite soft topology. The minimal soft [Formula: see text] (respectively, [Formula: see text]) is a soft topology in which each soft open (respectively, soft regular) filter base has only one adherent soft point and is convergent. Finally, the minimal soft [Formula: see text] topologies are subclasses of soft compact topologies.