Journal of Applied and Pure Mathematics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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ON FUZZY MAXIMAL, MINIMAL AND MEAN OPEN SETS

  • SWAMINATHAN, A. (Department of Mathematics, Government Arts College(Autonomous)) ;
  • SIVARAJA, S. (Department of Mathematics, Annamalai University)
  • 투고 : 2021.12.22
  • 심사 : 2022.02.07
  • 발행 : 2022.03.30
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초록

We have observed that there exist certain fuzzy topological spaces with no fuzzy minimal open sets. This observation motivates us to investigate fuzzy topological spaces with neither fuzzy minimal open sets nor fuzzy maximal open sets. We have observed if such fuzzy topological spaces exist and if it is connected are not fuzzy cut-point spaces. We also study and characterize certain properties of fuzzy mean open sets in fuzzy T1-connected fuzzy topological spaces.

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참고문헌

  1. C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182-190. https://doi.org/10.1016/0022-247x(68)90057-7
  2. B.M. Ittanagi and R.S. Wali, On fuzzy minimal open and fuzzy maximal open sets in fuzzy topological spaces, International J. of Mathematical Sciences and Applications 1 (2011), 1023-1037.
  3. R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. of Math. Anal. and Appl. 56 (1976), 621-633. https://doi.org/10.1016/0022-247x(76)90029-9
  4. Pu Pao-Ming and Liu Ying-Ming Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. of Math. Anal. and Appl. 76 (1980), 571-599. https://doi.org/10.1016/0022-247x(80)90048-7
  5. A. Swaminathan, Fuzzy mean open and fuzzy mean closed sets, J. Appl. Math. and Informatics 38 (2020), 463-468. https://doi.org/10.14317/JAMI.2020.463
  6. A. Swaminathan and S. Sivaraja, On fuzzy maximal, minimal open and closed sets, Advances in Mathematics:Scientific Journal 9 (2020), 7741-7747. https://doi.org/10.37418/amsj.9.10.5
  7. A. Swaminathan and S. Sivaraja, Fuzzy maximal and fuzzy minimal clopen sets, Advances in Mathematics:Scientific Journal 9 (2020), 9575-9581. https://doi.org/10.37418/amsj.9.11.61
  8. A. Swaminathan and S. Sivaraja, Fuzzy cut-point spaces, Annals of Communications in Mathematics 4 (2021), 126-130.
  9. L.A. Zadeh, Fuzzy sets, Information and control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X