Separation Axioms In Fuzzy Topological Spaces Pdf Download

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In this paper, the definition of the bipolar fuzzy (bf) point has been generalized, and using this, the concept of separation axioms has been introduced in bipolar fuzzy settings. Moreover, the relation between these separation axioms has been established.

their stronger forms. In [1,2], the notions of separation axioms Ti, i = 0 , 1, 2 , 3 , 4 , in L-topological spaces depend on the notions of fuzzy neighborhood filters, ordinary points and crisp closed subsets of X.

A fuzzy topology of a set X [3] is a subset t of LX which contains the constant fuzzy sets 0 and I, and closed with respect to finite intersection and arbitrary union. The pair (X, t ) is called a fuzzy topological space and the elements of t are called open

(b)In [2, p. 203], Lemma 5.1 states that "for every fuzzy topological space (X, t) and each x e X we have clx = x implies cl.{x} = {x} ". This statement has been used as a sufficient condition to prove that: ( 1) "every T3 -space is a T2 -space" (see [2, Proposition 5.1, p. 203]), and (li) "every T4 -space is a T.-space" (see [2, Proposition 6.1, p. 209]). In fact, the condition cl. {x} = {x} for all x e X is not equivalent to T1 -spaces. 2b1af7f3a8