Fuzzy Sᵦ-compactness and fuzzy Sᵦ-closed spaces
DOI:
https://doi.org/10.22199/issn.0717-6279-5838Keywords:
fuzzy set, fuzzy topology, fuzzy Sᵦ-compact space, fuzzy Sᵦ-open set, fuzzy Sᵦ-closed spaceAbstract
The aim of this paper is to introduce the notion of fuzzy Sβ -compactness. Some of the basic properties and characterization theorems would be investigated of this newly defined compactness in fuzzy setting. We would also introduce and study fuzzy Sβ - closed spaces.
References
M. E. Abd El-Monsef, S.N. El-Deeb and R. A. Mahmoud,”β-open sets and β-continuous mappings”, Bull. Fac. Sci., Assiut Univ., vol. 12, pp. 77-90, 1983.
M. E. Abd El-Monsef, A. M. Kozae, “Some generalized forms of compactness and closedness”, Delta Journal of Science, vol. 9, no. 2, pp. 257-269, 1985.
F. Alla, On fuzzy topological spaces, Ph. D. Thesis, Assiut Univ., Sohag, Egypt, 1984.
G. Balasubramanian, “On fuzzy β-compact spaces and fuzzy β-extremally disconnected spaces”, Kybernetika [cybernetics], vol. 33, no. 3, pp. 271-277, 1997.
B. Bhattacharya, J. Chakraborty and A. Paul, “γ∗-Hyperconnectedness in fuzzy topological spaces”, The Journal of Analysis, Vol. 28, pp. 9-19, 2020.
C. L. Chang, “Fuzzy topological spaces”, J. Math. Anal. Appl., Vol. 24, pp. 182-190, 1968.
D. Coker and A. Haydar Es, “On fuzzy S - closed spaces”, Doga Tu J. Math., pp. 145-152, 1987.
R. Dhar, “Some pairwise weakly fuzzy mappings”, Proyecciones (Antofagasta, On line), Vol. 38, No. 4, pp. 707-717, 2019.
R. Dhar, “Fuzzy Sβ-open sets and fuzzy Sβ-operations”, Acta Ciencia Indica, vol. 47, no. 1-4, pp. 57-66, 2021.
R. Dhar, “Continuity in fuzzy bitopological ordered spaces”, Proyecciones (Antofagasta, On line), vol. 40, no. 3, pp. 681-696, 2021.
R. Dhar, “Fuzzy Sβ - continuous and fuzzy Sβ - open mappings”, Proyecciones (Antofagasta, On line), vol. 41, no. 4, pp. 891-902, 2022.
A. Dutta and B. C. Tripathy, “On fuzzy b − θ - open sets in fuzzy topological space”, Journal of Intelligent and Fuzzy Systems, vol. 32, no. 1, pp. 137-139, 2017.
S. Ganguly and S. Saha, “A note on compactness in fuzzy setting”, Fuzzy Sets and Systems, vol. 34, pp. 117-124, 1990.
I. M. Hanafy, “Fuzzy β- compactness and fuzzy β- closed spaces”, Turk Journal of Mathematics, Vol. 28, pp. 281-293, 2004.
A. B. Khalaf and N. K. Ahmed, “Sβ-open sets and Sβ-continuity in topological spaces”, Thai Journal of Mathematics, vol. 11, no. 2, pp. 319-335, 2013.
P. M. Pu and Y. M. Liu, “Fuzzy topology. I. neighborhood structure of a fuzzy point and moore-smith convergence”, Journal of Mathematical Analysis and Applications, vol. 76, no. 2, pp. 571-599, 1980.
B. C. Tripathy and S. Debnath, “γ-open sets and γ-continuous mappings in fuzzy bitopological spaces”, Journal of Intelligent and Fuzzy Systems, vol. 24, no. 3, pp. 631-635, 2013.
B. C. Tripathy and G. C. Ray, “Mixed fuzzy ideal topological spaces” Applied Mathematics and Computations, vol. 220, pp. 602-607, 2013.
B. C. Tripathy and G. C. Ray, “Weakly continuous functions on mixed fuzzy topological spaces”, Act Scientiarum Technology, vol. 36, no. 2, pp. 331-335, 2014.
B. C. Tripathy and S. Debnath, “On fuzzy b - locally open sets in bitopological spaces”, Songklanakarin Journal of Science and Technology, vol. 37, no. 1, pp. 93-96, 2015.
T. H. Yalvac, “Fuzzy sets and functions on fuzzy topological spaces” Journal of Mathematical Analysis and Applications, Vol. 126, pp. 409-423, 1987.
L. A. Zadeh, “Fuzzy sets”, Information and Control, vol. 8, pp. 338-353, 1965.
Published
How to Cite
Issue
Section
Copyright (c) 2023 Runu Dhar
This work is licensed under a Creative Commons Attribution 4.0 International License.
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
