Some remarks on fuzzy infi topological spaces

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2021-02-0024

Keywords:

Fuzzy infi topological space, Fuzzy I-continuity, Fuzzy infi open mappings, Fuzzy infi closed mappings, Product fuzzy infi topology

Abstract

Induced fuzzy infi topological space is already introduced by Saha and Bhattacharya [Saha A.K., Bhattacharya D. 2015, Normal Induced Fuzzy Topological Spaces, Italian Journal of Pure and Applied Mathematics, 34, 45-56]. In this paper for the said space, we further analyse some properties viz. fuzzy I-continuity, fuzzy infi open mappings and fuzzy infi closed mappings etc. Also we study product fuzzy infi topological space and establish some results concerned with it.

Author Biographies

Birojit Das, National Institute of Technology Agartala

Dept. of Mathematics.

Baby Bhattacharya, National Institute of Technology Agartala

Dept. of Mathematics

Apu Kumar Saha, National Institute of Technology Agartala

Dept. of Mathematics.

References

M. Alimohammady and M. Roohi, “Compactness in fuzzy minimal spaces”, Chaos, solitons & fractals, vol. 28, no. 4, pp. 906-912, 2006, doi: 10.1016/j.chaos.2005.08.043

M. Alimohammady and M. Roohi, 2006, “Fuzzy minimal structure and fuzzy minimal vector spaces”, Chaos, solitons & fractals, vol. 27, no. 3, pp. 599-605, 2006, doi: 10.1016/j.chaos.2005.04.049

M. Alimohammady, E. Ekici, S. Jafari, and M. Roohi, “Fuzzy minimal separation axioms”, Journal of nonlinear sciences and applications, vol. 03, no. 03, pp. 157–163, 2010, doi: 10.22436/jnsa.003.03.01

G. Balasubramanian and P. Sundaram, “On some generalizations of fuzzy continuous functions”, Fuzzy sets and systems, vol. 86, no. 1, pp. 93–100, 1997, doi: 10.1016/0165-0114(95)00371-1

C. L. Chang, “Fuzzy topological spaces”, Journal of mathematical analysis and applications, vol. 24, no. 1, pp. 182–190, 1968, doi: 10.1016/0022-247X(68)90057-7

B. Das, A. K. Saha, and B. Bhattacharya, “On Infi-topological spaces”, Journal of fuzzy mathematics, vol. 25, no. 2, pp. 437-448, 2017.

S. Dang, A. Behera, and S. Nanda, “Some results on fuzzy supratopological spaces”, Fuzzy sets and systems, vol. 62, no. 3, pp. 333–339, 1994, doi: 10.1016/0165-0114(94)90117-1

R. Lowen, “Fuzzy topological spaces and fuzzy compactness”, Journal of mathematical analysis and applications, vol. 56, no. 3, pp. 621–633, 1976, doi: 10.1016/0022-247X(76)90029-9

H. Maki, J. Umehara, and T. Noiri, “Every topological space is pre T1/2”, Memoirs of the Faculty of Science Kochi University Series A Mathematics, vol. 17, pp. 33-42, 1996.

A. S. Masshour, A. A. Allam, F. S. Mahmud, and F. H. Khedr, “On supratopological spaces”, Indian journal of pure and applied mathematics, vol. 14, no. 4, pp. 502-510, 1983. [On line]. Available: https://bit.ly/3dUcp63

M. E. A. E. Monsef, and A. E. Ramadan, “On fuzzy supra topological spaces”, Indian journal of pure and applied mathematics, vol. 18, no. 4, pp. 322-329, 1987. [On line]. Available: https://bit.ly/3b12z0p

G. Palani Chetty, “Generalized fuzzy topology”, Italian journal of pure and applied mathematics, no. 24, pp. 91–96, 2008.

A. K- Saha, and D. Bhattacharya, “Normal induced fuzzy topological spaces”, Italian journal of pure and applied mathematics, no. 34, pp. 45-56, 2015. [On line]. Available: https://bit.ly/3r5JAaA

A. P. Šostak, “On a fuzzy topological structure”, Rendiconti del Circolo Matematico di Palermo, Serie II, Supplemento, no. 11, pp. 89-103, 1985. [On line]. Available: https://bit.ly/37T4IJL

B. C. Tripathy and G. C. Ray, “On δ-continuity in mixed fuzzy topological spaces”, Boletim da Sociedade Paranaense de Matemática, vol. 32, no. 2, pp. 175, 2014, doi: 10.5269/bspm.v32i2.20254

B. C. Tripathy and G. C. Ray, “Mixed fuzzy ideal topological spaces”, Applied mathematics and computation, vol. 220, pp. 602–607, 2013, doi: 10.1016/j.amc.2013.05.072

B. C. Tripathy and G. C. Ray, “Fuzzy δ∗-almost continuous and fuzzy δ∗-continuous functions in mixed fuzzy ideal topological spaces,” Proyecciones (Antofagasta), vol. 39, no. 2, pp. 435–449, 2020, doi: 10.22199/issn.0717-6279-2020-02-0027

L. A. Zadeh, “Fuzzy sets”, Information and control, vol. 8, no. 3, pp. 338–353, 1965, doi: 10.1016/S0019-9958(65)90241-X

Published

2021-03-01

How to Cite

[1]
B. Das, B. Bhattacharya, and A. K. Saha, “Some remarks on fuzzy infi topological spaces”, Proyecciones (Antofagasta, On line), vol. 40, no. 2, pp. 399-415, Mar. 2021.

Issue

Section

Artículos

Most read articles by the same author(s)