Advances in Fuzzy Systems — Applications and Theory - Vol. 9
FUZZY TOPOLOGY
by Liu Ying-Ming & Luo Mao-Kang (Sichuan Union University)
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.
Contents:
- Fuzzy Topological Spaces
- Operations on Fuzzy Topological
Spaces
- L-Valued Stratification Spaces
- Convergence Theory
- Connectedness
- Some Properties Related to Cardinals
- Separation (I)
- Separation (II)
- Compactness
- Compactification
- Paracompactness
- Uniformity and Proximity
- Metric Spaces
- Relations Between Fuzzy Topological Spaces and Locales
Readership: Senior undergraduates, graduate students, and researchers
in mathematics and computer science.
"This will be a very useful reference book for everyone working in this field."
| Mathematical Reviews, 1999 |
| 364pp |
Pub. date: Feb 1998 |
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