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Periodica Mathematica Hungarica

, Volume 26, Issue 1, pp 31–42 | Cite as

Fuzzy (Θ, S)-continuity and fuzzy (Θ, S)-closed graphs

  • M. E. Abd El-Monsef
  • I. M. Hanafy
  • S. N. El-Deeb
Article
  • 22 Downloads

Abstract

The concept of (ϑ,s)-continuity [6] is considered and studied in fuzzy setting. It is seen that althought it is independent with each of the concepts of fuzzy continuity [2], fuzzy σ-continuity [10], fuzzy almost continuity [1] and fuzzy semicontinuity [1]; it implies fuzzy weak continuity [1], but the converse may not be true. The image of a compact fts [2] under a fuzzy (ϑ,s)-continuous surjective function isS-closed [5]. Finally the concepts of fuzzy (ϑ,s)-closed graphs, fuzzy (ϑ,s)-T 2 spaces and fuzzy Urysohn spaces are introduced and mainly their connections with fuzzy (ϑ,s)-continuity are studied.

Mathematics subject classification numbers, 1991

Primary. 54A40 Secondary 54C10 

Key words and phrases

Fuzzy topological spaces Compactness S-closeness and fuzzy continuities 

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References

  1. [1]
    K. K. Azad, On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity,J. Math. Anal. Appl. 82 (1981), 14–32.Google Scholar
  2. [2]
    C. L. Chang, Fuzzy topological spaces,J. Math. Anal. Appl. 24 (1968), 182–189.Google Scholar
  3. [3]
    T. E. Ganter, R. C. Steinlage andR. H. Warren, Compactness in fuzzy topological spaces,J. Math. Anal. Appl. 62 (1976), 547–562.Google Scholar
  4. [4]
    B. Hutton andI. L. Reilly, Seperation axioms in fuzzy topological spaces,Department of Mathematics, University of Auckland, Report, No.55 March 1974.Google Scholar
  5. [5]
    A. S. Mashhour, F. H. Khedr andF. M. Zeyada, On fuzzyS-closed spaces and fuzzy almost-compact spaces,Bull. Fac. Sci., Assuit Univ.,15(1) (1986), 137–146.Google Scholar
  6. [6]
    J. E. Joseph andM. H. Kwack, OnS-closed spaces,Proc. Amer. Math. Soc.,80 (2) (1980), 341–348.Google Scholar
  7. [7]
    A. K. Katsaras andD. B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces.J. Math. Anal. Appl. 58 (1977), 135–146.Google Scholar
  8. [8]
    Pu Pao-Ming andLin Ying-Ming, Fuzzy topology I. Neighbourhood structure of a fuzzy point and Moor-Smith convergence,J. Math. Anal. Appl.,76 (1980), 571–599.Google Scholar
  9. [9]
    R. Srivastava, S. N. Lal andA. K. Srivastava, Fuzzy Hausdorff spaces,J. Math. Anal. Appl.,81 (1981), 497–506.Google Scholar
  10. [10]
    Supriti Saha, Fuzzy σ-continuous mappings,J. Math. Anal. Appl.,126 (1987), 130–142.Google Scholar
  11. [11]
    C. K. Wong, Fuzzy points and local properties of fuzzy topology,J. Math. Anal. Appl.,46, (1974), 316–328.Google Scholar
  12. [12]
    L. A. Zadeh, Fuzzy sets,Inform. Control 8 (1965), 338–353.Google Scholar

Copyright information

© Akadémiai Kiadó 1993

Authors and Affiliations

  • M. E. Abd El-Monsef
    • 1
  • I. M. Hanafy
    • 1
  • S. N. El-Deeb
    • 2
  1. 1.Mathematic Department Faculty of ScienceTanta UniversityTantaEgypt
  2. 2.Mathematic Department Alfaun Faculty EducationCairo UniversityCairoEgypt

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