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2020ā€¢International Journal of ADVANCED AND APPLIED SCIENCESOpen access

Separation axioms on fuzzy ideal topological spaces in š‘ŗ ostakā€˜s sense

Fahad Alsharari, Yaser Saber

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Abstract

In the present paper, we introduce the notions of š‘Ÿ-fuzzy ā‹†-open and š‘Ÿ-fuzzy ā‹†-closed sets in Å ostak's fuzzy topological spaces.Also, we study some properties of these notions.Moreover, we give the concept of fuzzy ideal ā‹†irresolute mapping in Å ostak's fuzzy topological spaces.Finally, we study some kinds of separation axioms namely r -FIR š‘– where i={0. 1. 2. 3} and r -FIT š‘— where j={1.2. 2 1 2 .3. 4} and the relations between them.Also, some of their characterizations and several of fundamental properties have been established.

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In the present paper, we introduce the notions of š‘Ÿ-fuzzy ā‹†-open and š‘Ÿ-fuzzy ā‹†-closed sets in Å ostak's fuzzy topological spaces.Also, we study some properties of these notions.Moreover, we give the concept of fuzzy ideal ā‹†irresolute mapping in Å ostak's fuzzy topological spaces.Finally, we study some kinds of separation axioms namely r -FIR š‘– where i={0. 1. 2. 3} and r -FIT š‘— where j={1.2. 2 1 2 .3. 4} and the relations between them.Also, some of their characterizations and several of fundamental properties have been established.

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Available abstract

In the present paper, we introduce the notions of š‘Ÿ-fuzzy ā‹†-open and š‘Ÿ-fuzzy ā‹†-closed sets in Å ostak's fuzzy topological spaces.Also, we study some properties of these notions.Moreover, we give the concept of fuzzy ideal ā‹†irresolute mapping in Å ostak's fuzzy topological spaces.Finally, we study some kinds of separation axioms namely r -FIR š‘– where i={0. 1. 2. 3} and r -FIT š‘— where j={1.2. 2 1 2 .3. 4} and the relations between them.Also, some of their characterizations and several of fundamental properties have been established.

Key concepts: Separation axiom, Mathematics, Topological space, Ideal (ethics), Axiom, Fuzzy logic, Pure mathematics, Topology (electrical circuits)

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Separation axioms on fuzzy ideal topological spaces in š‘ŗ ostakā€˜s sense ā€” Research Paper | ScholarLens