## Fuzzy TopologyImparts developments in various properties of fuzzy topology viz., fuzzy set theory, fuzzy point and its neighbourhood structure, Fuzzy nets and Fuzzy convergence, Fuzzy metric, Different fuzzy compactness, Fuzzy connectedness, Fuzzy separation axioms and properties, Product spaces, Convex fuzzy sets and Fuzzy uniform spaces. |

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### Contents

Fuzzy Set Theory | 1 |

Fuzzy Topological Spaces | 15 |

Fuzzy Product Induced Spaces | 32 |

Copyright | |

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### Common terms and phrases

a-compact a-cuts a-shading accumulation point axiom called a fuzzy closed fuzzy set closure operator compact space continuous function convex fuzzy cone convex fuzzy set countable Counterexample crisp sets defined Definition denote directed sets easily seen exists a fuzzy exists an element exists an open family of fuzzy fi(x follows at once fuzzy closed sets fuzzy compact space fuzzy continuously converges fuzzy hyperplane fuzzy logic fuzzy open Q-neighborhood fuzzy open sets fuzzy point fuzzy pseudo-metric space fuzzy regular fuzzy space fuzzy subset fuzzy subspace fuzzy topological space fuzzy uniform space Hence hyperplane If(X initial topology intersection Lemma lim supD(K lower semicontinuous mapping Math membership function metric space Obviously open fuzzy set Proof Proposition prove Q-separated quasi-coincident quasi-discoincident real numbers resp separation axiom strong fuzzy compact subbase Suppose T2 space Theorem unit interval weakly fuzzy compact Xand