On Single-Valued Neutrosophic Proximity Spaces

Abstract

In this paper, the notion of single-valued neutrosophic proximity spaces which is a generalisation of fuzzy proximity spaces [Katsaras AK. Fuzzy proximity spaces. Anal and Appl. 1979;68(1):100-110.] and intuitionistic fuzzy proximity spaces [Lee SJ, Lee EP. Intuitionistic fuzzy proximity spaces. Int J Math Math Sci. 2004;49:2617-2628 was introduced and some of their properties were investigated. Then, it was shown that a single-valued neutrosophic proximity on a set X induced a single-valued neutrosophic topology on X. Furthermore, the existence of initial single-valued neutrosophic proximity structure is proved. Finally, based on this fact, the product of single-valued neutrosophic proximity spaces was introduced.