A Study of Alexandroff Compactification within the Framework of Near Soft Topological Spaces

Abstract

Near sets and near soft sets are powerful tools for quantifying the proximity of collections of objects and for constructing innovative topological frameworks. Compactification is considered a central concept in topology. In this study, we introduce the Alexandroff near soft compactification. The main results are as follows:

1. Every near soft topological space is near soft compact (Theorem 4.12).

2. A near soft topological space $({F_A}^n,A,{\tau}^n)$ is a near soft Hausdorff compactification of $(F_A, A,\tau)$ if and only if $(F_A, A,\tau)$ is both near soft locally compact and near soft Hausdorff (Theorem 4.13).