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Issue:R1 and level R1 separation axioms on intuitionistic fuzzy pairwise topological spaces using intuitionistic fuzzy open sets

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Title of paper: R1 and level R1 separation axioms on intuitionistic fuzzy pairwise topological spaces using intuitionistic fuzzy open sets
Author(s):
Saikh Shahjahan Miah     0000-0002-9182-5299
Department of Mathematics, Faculty of Science, Mawlana Bhashani Science and Technology University, Tangail-1902, Bangladesh
skhshahjahan@gmail.com
Md. Hridoy Hasan     0009-0007-5085-9357
Department of Mathematics, Faculty of Science, Mawlana Bhashani Science and Technology University, Tangail-1902, Bangladesh
hridoyhasan89@gmail.com
Ruhul Amin     0009-0003-6664-5311
Department of Mathematics, Begum Rokeya University, Rangpur-5404, Bangladesh
ruhulamin@brur.ac.bd
Nigar Sultana     0000-0003-0848-8015
Department of Mathematics, Faculty of Science, Mawlana Bhashani Science and Technology University, Tangail-1902, Bangladesh
Department of Mathematics, North Carolina State University, Raleigh, NC, USA
nigarsultana262@gmail.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 3, pages 290–304
DOI: https://doi.org/10.7546/nifs.2025.31.3.290-304
Download:  PDF (256  Kb, File info)
Abstract: This study investigates the notions of intuitionistic fuzzy (IF) R1 pairwise topological space and α-R1 type separation axioms on IF pairwise topological spaces in the sense of intuitionistic fuzzy open sets. We define four notions of IF R1 pairwise topological space and three notions of α-R1 IF pairwise topological spaces and show the relationship among the notions separately with appropriate examples. In order to show the correctness of the proposed definitions, we show the good extension property for both types of the notions followed by examples as well. Finally, we show that our notions satisfy the hereditary and preserve the homeomorphism mapping properties.
Keywords: Intuitionistic fuzzy set (IFS), Intuitionistic fuzzy pairwise topological space, Separation axiom, R1 Intuitionistic fuzzy pairwise topological space, Good extension.
AMS Classification: 03E72, 54A40, 94D05.
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