Generalized Boundary Closed Sets in Fuzzy Topological Spaces

Sanjivappa K Dembare1

1Department of Mathematics, Government first Grade College, Navanagar, Bagalkot, Karnataka, India.

Abstract: In this paper, fuzzy boundary generalized closed set is introduced and studied. It is proved that every fuzzy closed set and fuzzy boundary closed set is fuzzy Boundary generalized closed set but the converses need not be true. Every fbg-closed set is fspg-closed, every fgs-closed and fpg-closed sets is fbg- closed, but the converses need not be true.
Keywords: Fuzzy set, Fuzzy Boundary set, Fuzzy Closed set, Fuzzy open set.

Cite this article as: Sanjivappa K Dembare, Generalized Boundary Closed Sets in Fuzzy Topological Spaces, Int. J. Math. And Appl., vol. 9, no. 3, 2021, pp. 55-60.

  1. N. Levine, Generalized closed sets in topology, Rendiconti del Circolo Matematico di Palermo, 19(1970), 89-96.
  2. S. P. Arya and T. Nour, Characterizations of s-normal spaces, Indian J.Pure Appl. Math., 21(1990), 717-719.
  3. S. G. Crossley and S. K. Hildebrand, Semi topological properties, Fund. Math.,74(1972), 233-252.
  4. J. Dontchev, On-generalizing-semi-preopesets, Univ. Ser. A. Math., 16(1995), 35-48.
  5. H. Maki, J. Umehara and T. Noiri, Every Topological space is pre $T_{1/2}$, Memoirs of the Faculty of Science, Kochi University, 17(1996), 33-42.
  6. S. R. Malgan, Generalized closed maps, J. Karnatak University, 27(1982), 82-88.
  7. N. Palaniappan and K. C. Rao, Regular generalized closed Sets, Kyungpook Math. J., 33(2)(1993), 211-219.
  8. A. Noiri, A generalization of closed mappings, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 54(1973), 412-415.
  9. Dunham, A new closure operator for non-$T_{1}$ topologies, Kyungpook Math. J., 22(1982), 55-60.
  10. P. Sundram and Sheik John, On w-closed sets in topology, Acta Ciencia Indica, 4(2000), 389-392.
  11. L. A. Zadeh, Fuzzy sets, Information and Control, 8(1965) 338-353.
  12. G. J. Klir and B. Yuan, Fuzzy sets and fuzzy logic theory and application, PHI, (1957).
  13. C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24(1968), 182-190.
  14. Richard H. Warren, Boundary of a fuzzy set, Indiana University Mathematics Journal, 26(2)(1977), 191-197.
  15. R. S. Wali and Vivekananda Dembre, On pre generalized pre regular weakly closed sets in topological spaces, Journal of Computer and Mathematical Science, 6(2)(2015), 113-125.
  16. G. Balasubramaniam and P. Sundaram, On some generalizations of fuzzy continuous functions, Fuzzy Sets and Systems, 86(1997), 93-100.
  17. A. S. Bin Shahana, Mappings in fuzzy topological spaces, Fuzzy Sets and Systems, 61(1994), 209-213.
  18. S. R. Malgan and S. S. Benchalli, Open maps, closed maps and local compactness in fuzzy topological spaces, J. Math. Anal., 99(1984), 338-349.