## A fuzzy version of Tietze's extension theoremShow full item record

Title | A fuzzy version of Tietze's extension theorem |
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Author | Reagor, Mary Evelyn Pensworth |

Date | 1983 |

Genre | Dissertation |

Degree | Doctor of Philosophy |

Abstract | The following theorem generalizing Tietze's Extension Theorem for real-valued functions is proved. Theorem. Let (X,(tau)) be an L-fuzzy topological space. If X is normal and fuzzy subsets K and K (WEDGE) K' are closed in X, and f : X (--->) {0.1}(L) is an L-fuzzy continuous function on K (LESSTHEQ) X , then there exists F : X (--->) {0,1}(L), an L-fuzzy continuous extension of f to X , such that (F(VBAR)K)('-1)(0+) (LESSTHEQ) F(0+) (LESSTHEQ) F(1-) (LESSTHEQ) (F(VBAR)K)('-1)(1-) (V) K'. Throughout the paper the conceptual difficulties of generalizing standard topological terms to L-fuzzy topological terms are discussed. In particular, a theory of relative topologies and relative functions for L-fuzzy topological spaces is developed. The extension of a relative L-fuzzy continuous function into the fuzzy unit interval is defined. The equivalence of L-fuzzy continuous functions and monotone families of open sets is proved. This equivalence is exploited to establish a fuzzy version of Tietze's Extension Theorem. A partial converse to the theorem is proved. |

Link | https://repository.tcu.edu/handle/116099117/33836 |

Department | Mathematics |

Advisor | Addis, David F. |

##### This item appears in the following Collection(s)

- Doctoral Dissertations [1437]

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