Abstract

The study of the relationship between fuzzy topological and order structures was initiated by Katsaras in [ J. Math. Anal. Appl. 84 (1981) 44–58]. In [M.Y. Bakier et al. Proc. of Assiut First Intern. Conf., Part VIII (1990) 41–61] some properties of these spaces are studied. In [M.Y. Bakier and K. El-Saady, Fuzzy Sets and Systems 54 (1993) 213–220] is, by similar manner introduced the idea of order in fuzzy topological vector spaces. In another work of A.S. Mashhour et al. the study of the relationship between order and Lowen-fuzzy uniformities is introduced and many results are studied. In this paper, by similar manner, we will introduce the idea of order in both the fuzzy proximity space and the fuzzy syntopogenous space and we study some properties of these spaces.

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