On lower separation axioms

Abstract

In [3] Mashhour et al. introduced the concept of fuzzy disjointness. Two fuzzy sets A, B in X are said to be fuzzy disjoint if A ⩽ co B, where co B is the complement of B. Using this concept, they introduced FT i separation axioms as a generalization for the basic separation axioms T i ( i = 1, …, 4). In [5] Singal and Rajvanshi used the concepts of regular open fuzzy sets [1] and fuzzy disjointness to introduce some fuzzy almost separation axioms which are stronger than those of Mashhour. Unfortunately, some results in [5] are incorrect. In this paper, we use the concept of the quasi-coincident relation [4] to restate lower fuzzy separation axioms and give a corrected version for some definitions and results in [5].