Title of paper:

Intuitionistic fuzzy based regular and normal spaces

Author(s):

Tamanna Tasnim Prova

Department of Mathematics, Rajshahi University of Engineering and Technology, Rajshahi6204, Bangladesh

tprova.ku@gmail.com

Md. Sahadat Hossain

Department of Mathematics, University of Rajshahi, Rajshahi6205, Bangladesh

sahadat@ru.ac.bd


Published in:

Notes on Intuitionistic Fuzzy Sets, Volume 26 (2020), Number 4, pages 53–63

DOI:

https://doi.org/10.7546/nifs.2020.26.4.5363

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Abstract:

In this paper, we define the notion of intuitionistic fuzzy based regular and normal spaces. We also study that classical regular and normal spaces are also intuitionistic fuzzy based regular and normal spaces but the converses are not true in general. This notion opens up a new conception of generalization of classical regular and normal spaces. The hereditary and topological properties of intuitionistic fuzzy based regular and normal spaces have been also investigated. Moreover, by setting some examples we show that every intuitionistic fuzzy based regular space as well as intuitionistic fuzzy based normal space need not be T_{1} spaces. Finally, it is shown that under some conditions the images and homeomorphic images are preserved in intuitionistic fuzzy based regular and normal spaces.

Keywords:

Intuitionistic fuzzy based set, Intuitionistic fuzzy based topological space, Hereditary, Regular space, Normal space.

AMS Classification:

54A05, 54C50.

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