Some types of pairwise soft sets and the associated soft topologies

Article type: Research Article

Authors: Kandil, A.^a | Tantawy, O.A.E.^b | El-Sheikh, S.A.^c | Hazza, Shawqi A.^{d; *}

Affiliations: [a] Department of Mathematics, Faculty of Science, Helwan University, Helwan, Egypt | [b] Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt | [c] Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt | [d] Department of Mathematics, Faculty of Education, Taiz University, Taiz, Yemen

Correspondence: [*] Corresponding author. Shawqi A. Hazza, Department of Mathematics, Faculty of Education, Taiz University, Taiz, Yemen. Tel.: +967 737437297; E-mail: [email protected].

Abstract: In this paper, we introduce the notions of pairwise soft sub kernel, and pairwise ∨-soft sets in a soft bitopological space (X, η1, η2, E). Also, we study the fundamental properties of pairwise ∨-soft sets and we investigate the associated soft topology ηp∨. Moreover, we introduce the notions of generalized pairwise Λ(∨)-soft sets and we investigate their basic properties. Also, we define a soft closure operator on the family of all generalized pairwise Λ-soft sets and generate, in usual manner, an Alexandroff soft topology ηgpΛ on X which is finer than ηp∨. Furthermore, we prove that (X, ηgpΛ, E) is always a soft T12 space. In addition, we introduce characterizations of pairwise soft T12* by using generalized pairwise Λ-soft sets and we show that the concepts of generalized pairwise Λ-soft set and generalized pairwise closed soft set are independent.

Keywords: Soft sets, soft topology, soft bitopology, soft bitopological spaces, pairwise soft sets, pΛ-soft sets, p∨-soft sets, gpΛ-soft sets, gp∨-soft sets, soft T_1/2 spaces, pairwise soft T^*_1/2 spaces and soft separation axioms

DOI: 10.3233/JIFS-16180

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 1, pp. 1007-1018, 2017