Intuitionistic regular subspaces in intuitionistic topological spaces

Md. dalim Haque, Nasima Akhter, Md. Masum Murshed

Abstract


This paper explores the concept of intuitionistic topological spaces, delving into their definitions and essential properties. It also examines intuitionistic topological subspaces, providing insights into their characteristics. Additionally, the paper investigates intuitionistic regular spaces and demonstrates their hereditary nature, specifically focusing on  and . To illustrate these concepts in practical terms, the paper presents two real-world examples of intuitionistic sets. Through a comprehensive analysis of intuitionistic topological spaces and their subsets, the study sheds light on the inheritability of regularity in these spaces. Furthermore, the work emphasizes the significance of intuitionistic topological spaces within the realm of mathematical research, showcasing their applicability through concrete instances of intuitionistic sets.


Keywords


Intuitionistic Set; Intuitionistic Topological Space; Relative Intuitionistic Topology; Intuitionistic Regular Subspace.

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References


Atanassov, K. (1983). Intuitionistic fuzzy sets. VII ITKR’s Session. Sofia.

Bayhan, S., & Çoker, D. (2001). On separation axioms in intuitionistic topological spaces. International Journal of Mathematics and Mathematical Sciences, 27(10). https://doi.org/10.1155/s0161171201004884

Chae, G. B., Kim, J., Lee, J. G., & Hur, K. (2020). Interval-valued intuitionistic sets and their application to topology. Annals of Fuzzy Mathematics and Informatics.

Çoker, D. (1996). A note on intuitionistic sets and intuitionistic points. Turkish Journal of Mathematics, 20(3).

Çoker, D. (1997). An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems, 88(1). https://doi.org/10.1016/S0165-0114(96)00076-0

Çoker, D. (2000). An introduction to intuitionistic topological spaces. BUSEFAL, 81, 51–56.

Haque, Md. D., Akhter, N., & Murshed, Md. M. (2022). Intuitionistic subspaces in intuitionistic topological spaces. International Journal of Scientific & Engineering Research, 13(8), 1266–1270.

Ilango, G., & Albinaa, T. A. (2016). Properties of α-interior and α-closure in intuitionistic topological spaces. IOSR Journal of Mathematics (IOSR-JM), 12(6), 91–95.

Islam, Md. S., Hossain, Md. S., & Mahbub, Md. A. (2021). On intuitionistic fuzzy r-regular spaces. International Journal of Fuzzy Mathematical Archive, 19(02). https://doi.org/10.22457/ijfma.v19n2a05234

Yaseen, Y. J., & Mohammad, R. A. (2012). Regular and weak regular in intuitionistic topological spaces. Journal of University of Anbar for Pure Science, 6(3). https://doi.org/10.37652/juaps.2012.82139

Jassim, T. H. (2013). Completely normal and weak completely normal in intuitionistic topological spaces. International Journal of Scientific & Engineering Research, 4(10), 438–442.

Kim, J. H., Lim, P. K., Lee, J. G., & Hur, K. (2017). Intuitionistic topological space. Annals of Fuzzy Mathematics and Informatics.

Prova, T. T., & Hossain, Md. S. (2020). Intuitionistic fuzzy based regular and normal spaces. Notes on Intuitionistic Fuzzy Sets, 26(4), 53–63.

Selvanayaki, S., & Ilango, G. (2015). Igpr-continuity and compactness intuitionistic topological spaces. British Journal of Mathematics & Computer Science, 11(2). https://doi.org/10.9734/bjmcs/2015/19568

Selvanayaki, S., & Ilango, G. (2016). Homeomorphism on intuitionistic topological spaces. Annals of Fuzzy Mathematics and Informatics, 11(6), 957–966.

Zadeh, L. A. (1965). Fuzzy sets, information and control. 8(3), 338–353. https://doi.org/https://doi.org/10.1016/S0019-9958(65)90241-X




DOI: http://dx.doi.org/10.24042/djm.v6i2.17817

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Desimal: Jurnal Matematika is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.