Soft sets over power sets: Generalities and applications to topology

Abstract

The concept of soft set theory was introduced by D. Molodtsov in 1999 for modeling uncertainty. In [13] a special kinds of soft sets, namely soft neighborhood set, was defined and the relations between this concept and classical topology was given. In this paper, our aim is to extend the studies in [13]. We study on some properties of compactness and lower separation axioms in soft neighborhood sets and generalize Alexander subbase theorem and Tychonoff theorem to soft neighborhood sets.