Abstract
Separation axioms on fuzzy ideal topological spaces in 𝑺 ̆ ostak‘s sense
Highlights
We introduce the notions of r-fuzzy ⋆-open and r-fuzzy
A fuzzy point xt is said to be quasi-coincident with a fuzzy set A ∈ IX denoted by xtqA, if t + A(x) > 1
Cl⋆(B2. r) ≤ 1 − B ≤ 1 − Cl⋆(B1. r), that is, it investigated some kinds of separation axioms namely r − FIRi where i={0, 1, 2, 3} and r − FIRj where j={1, 2, 2 1, 3, 4} as well as some of their characterizations and fundamental properties
Summary
A fuzzy point xt is said to be quasi-coincident with a fuzzy set A ∈ IX denoted by xtqA, if t + A(x) > 1. (3) r − FIR2 iff xtqD = Cl⋆(D. r) implies there exist r-fuzzy ⋆-open sets A, B ∈ IX such that xt ∈ A, D ≤ B and AqB. (5) r − FIT1 iff xtqys implies that there exists a rfuzzy ⋆-open set A ∈ IX such that xt ∈ A and ysqA. (7) r − FIT212 iff xtqys implies that there exist r-fuzzy ⋆-open sets A. Since r-FIR 2 and r − FIT1, are both in X, there exists a r-fuzzy ⋆-open set D ∈ IX such that xt ∈ D and ysqD. By (2), there exists a r-fuzzy ⋆-open set B1 ∈ IX, such that xt ∈ B1 ≤ Cl⋆(B1. Cl⋆(B2. r) ≤ 1 − B ≤ 1 − Cl⋆(B1. r), that is, it investigated some kinds of separation axioms namely r − FIRi where i={0, 1, 2, 3} and r − FIRj where j={1, 2, 2 1 , 3, 4} as well as some of their characterizations and fundamental properties
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