Soft sets over power sets: Generalities and applications to topology

Article type: Research Article

Authors: Varol, Banu Pazar^* | Aygün, Halis

Affiliations: Department of Mathematics, University of Kocaeli, Umuttepe Campus, Kocaeli, Turkey

Correspondence: [*] Correspondence to: Banu Pazar Varol, Department of Mathematics, University of Kocaeli, Umuttepe Campus, 41380 Kocaeli, Turkey. Tel.: +90 505 387 0815; E-mail: [email protected].

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.

Keywords: Soft set, soft neighborhood set, topology, compactness

DOI: 10.3233/IFS-151605

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 1, pp. 389-395, 2015