Fuzzy Topology

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World Scientific, 1997 - Mathematics - 353 pages
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Fuzzy 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
Bibliography
327
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