## Fuzzy TopologyFuzzy set theory provides us with a framework which is wider than that of classical set theory. Various mathematical structures, whose features emphasize the effects of ordered structure, can be developed on the theory. Fuzzy topology is one such branch, combining ordered structure with topological structure. This branch of mathematics, emerged from the background — processing fuzziness, and locale theory, proposed from the angle of pure mathematics by the great French mathematician Ehresmann, comprise the two most active aspects of topology on lattice, which affect each other.This book is the first monograph to systematically reflect the up-to-date state of fuzzy topology. It emphasizes the so-called “pointed approach” and the effects of stratification structure appearing in fuzzy sets.The monograph can serve as a reference book for mathematicians, researchers, and graduate students working in this branch of mathematics. After an appropriate rearrangements of the chapters and sections, it can also be used as a text for undergraduates. |

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### Contents

Fuzzy Topological Spaces | 32 |

Operations on Fuzzy Topological Spaces | 60 |

Lvalued Stratification Spaces | 73 |

Convergence Theory | 94 |

Connectedness | 116 |

Some Properties Related to Cardinals | 124 |

Separation I | 134 |

Separation II | 151 |

Compactness | 187 |

Compactification | 210 |

Uniformity and Proximity | 247 |

Metric Spaces | 285 |

Relations between Fuzzy Topological Spaces and Locales | 308 |

327 | |

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### Common terms and phrases

A G Lx adherent point arbitrary join preserving base called closed subset cluster point compactification complete lattice completely distributive lattice completely regular conditions are equivalent countable crisp defined Definition Let Lx,6 denote e-regular element exists an L-fuzzy F-lattice F-ts family of L-fts flintily locally finite following conditions fulfils fuzzy compact fuzzy topological spaces G M(L hence homeomorphism induced spaces interior operator isomorphism join-semilattice L-fuzzy continuous mapping L-fuzzy mapping L-fuzzy p.q. metric L-fuzzy point L-fuzzy quasi-uniformity L-fuzzy space L-fuzzy subset L-fuzzy topology L-fuzzy uniformity Lemma Let Let Lx locally finite lower semicontinuous Lx,S LY,n M(LX meet-semilattice metric space minimal set molecule N-compact need only prove neighborhood open a-Q-cover open subset order-reversing order-reversing involution ordinary topological space paracompact partial order poset pr(L Q(xa quasi-coincides stratified strongly compact subbase subfamily subspace surjective Take Theorem Let Lx,6 topological order

### References to this book

Advances in Spatio-Temporal Analysis Xinming Tang,Yaolin Liu,Jixian Zhang,Wolfgang Kainz No preview available - 2007 |