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

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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.

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Authors and Affiliations

  1. Mathematic Department Faculty of Science, Tanta University, Tanta, Egypt

    M. E. Abd El-Monsef & I. M. Hanafy

  2. Mathematic Department Alfaun Faculty Education, Cairo University, Alfaun, Cairo, Egypt

    S. N. El-Deeb

Authors
  1. M. E. Abd El-Monsef
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  2. I. M. Hanafy
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  3. S. N. El-Deeb
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Abd El-Monsef, M.E., Hanafy, I.M. & El-Deeb, S.N. Fuzzy (Θ, S)-continuity and fuzzy (Θ, S)-closed graphs. Period Math Hung 26, 31–42 (1993). https://doi.org/10.1007/BF01875879

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  • DOI: https://doi.org/10.1007/BF01875879

Mathematics subject classification numbers, 1991

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