New Boundary Function In Fuzzy Topological Spaces

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-6
Year of Publication : 2021
Authors : Sanjivappa K Dembare
  10.14445/22315373/IJMTT-V67I6P507

MLA

MLA Style: Sanjivappa K Dembare  "New Boundary Function In Fuzzy Topological Spaces" International Journal of Mathematics Trends and Technology 67.6 (2021):50-57. 

APA Style: Sanjivappa K Dembare(2021). New Boundary Function In Fuzzy Topological Spaces International Journal of Mathematics Trends and Technology, 50-57.

Abstract
In this Paper the notion of fuzzy boundary generalized-continuity, fuzzy boundary generalized-irresolute mappings,fuzzy boundary generalized - homeomorphism and fuzzy boundary generalized*-homeomorphism are introduced and some characterizations are obtained. It is shown that f-continuous map is fuzzy boundary generalized-continuous, fuzzy boundary generalized-irresolute map is fuzzy boundary generalized-continuous, fuzzy boundary generalized-continuous map is fgb-continuous and fuzzy boundary generalized-continuous is fspg-continuous, but the converses need not be true in each of the cases which is shown by examples.

Reference

[1] Levine, Generalized closed sets in topological spaces, Rend.circMat.Palermo (3)19(1970)
[2] S.P.Arya and T.Nour, Indian J.Pureappl.Math21 (1990)717-19
[3] S.G.CrossleyandS.K.Hildebrand, Semi topological properties, Fund.math,74(1972)233-254.
[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 T½ mem Fac sci, Kochi univ,Math ,17 1996,33-42.
[6] S.R.Malgan, Generalized closed maps,J.Karnatak University,sci 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,acad.naz.lincei rend.cl.scifis.mat.natur.,54(1973),412-415.
[9] Dunham, a new closure operator for non-T1 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] A.N.Zahren, J. Fuzzy math 2 (1994) 579-586.
[13] G.J.Klir,B.Yuan, fuzzy sets and fuzzy logic theory and application,PHI(1957).
[14] C.L.Chang,Fuzzy topological spaces,JI.Math.Anal.Appl.,24(1968)182-190
[15] Boundary of a fuzzy set, Indian University mathematics Journal Vol.26,No.2(1977)
[16] R.S.Wali and Vivekananda Dembre, on pre generalized pre regular weakly closed sets in topological spaces, Journal of computer and Mathematical science Vol 6 , issue 2, 28 Feb 2015
[17] G. Balasubramaniam and P. Sundaram, on some generalizations Of fuzzy continuous functions, fuzzy sets and systems,86 (1997) 93-100.
[18] A. S. Bin shahana, mappings in fuzzy topological spaces, fuzzy Sets and systems 61 (1994) 209-213.
[19] 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

Keywords : Fuzzy boundary closed sets, Fuzzy boundary open sets, fuzzy boundary generalized-continuity, fuzzy boundary generalized homeomorphism.