In recent years, many concepts in mathematics, engineering, computer science, and many other disciplines have been in a sense redefined to incorporate the notion of fuzziness. Designed for graduate students and research scholars, Fuzzy Topology imparts the concepts and recent developments related to the various properties of fuzzy topology.
The author first addresses fundamental problems, such as the idea of a fuzzy point and its neighborhood structure and the theory of convergence. He then studies the connection between fuzzy topological spaces and topological spaces and introduces fuzzy continuity and product induced spaces. Chapter Three examines fuzzy nets, fuzzy upper and lower limits, and fuzzy convergence and is followed by a study of fuzzy metric spaces. The treatment then introduces the concept of fuzzy compactness before moving to initial and final topologies and the fuzzy Tychnoff theorem. The final sections of the book cover connectedness, complements, separation axioms, and uniform spaces.
Sprache
Verlagsort
Verlagsgruppe
Maße
Höhe: 229 mm
Breite: 152 mm
Gewicht
ISBN-13
978-0-8493-2416-1 (9780849324161)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Alagappa University, Karaikudi, India
FUZZY TOPOLOGICAL SPACES
Fuzzy Sets
Concept of a Fuzzy Point and its Neighborhood Structure
Fuzzy Points and Level Sets
Local Base-A Counter Example
Closure and Kuratowski's Theorem on 14 Sets
Accumulation Points: Generalization C.T. Yang's Theorem
Omega-Accumulation Points: Lindelof Property
Subspaces
FUZZY PRODUCT INDUCED SPACES
Fuzzy Product Spaces
The Functions W and I
Fuzzy Continuity
Product-Induced Spaces
FUZZY NETS AND FUZZY CONVERGENCE
Fuzzy Nets
Fuzzy Upper and Lower Limit
Uniqueness of Convergence Theorem on Iterated Limits
Fuzzy Subnets and Subsequences
A One-to-One Correspondence Between Convergence Classes and Fuzzy Topologies
Fuzzy Continuous Convergence
FUZZY METRIC SPACES
Fuzzy Metric Spaces
Fuzzy Metrization Theorem
Fuzzy Continuous Functions
FUZZY COMPACT SPACES
Quasi Fuzzy Compact Spaces
Weakly Fuzzy Compact Spaces
a-Compact Spaces
Strong Fuzzy Compact Spaces
Ultra-Fuzzy Compact Spaces
Fuzzy Compact Spaces
INITIAL AND FINAL FUZZY TOPOLOGIES
Initial Fuzzy Topologies
Final Fuzzy Topologies
A Comparison of Different Compactness Notions in Fuzzy Topological Spaces
Good Extensions
Product Theorems
Implications
CONNECTEDNESS IN FUZZY TOPOLOGICAL SPACES
Fuzzy Connectedness
An Alternative Characterization of i(d)
The Product Theorem for (c1) and (c2)
FUZZY SEPARATION
Set-Theoretic Approach
Separation Axioms
Separation
On Separation Axioms in Fuzzy Topological Spaces
Separation in Fuzzy Neighborhood Spaces
Separation Properties
Subspaces
PRODUCT SPACES
Product Spaces
Affine Fuzzy Sets
Dimension and Fuzzy Hyperplanes
Convex Fuzzy Sets
Fuzzy Separation Theorems
Fuzzy Separation
FUZZY UNIFORM SPACES
Introduction
Definitions and Fundamental Properties
The Operators wuxu
Initial Fuzzy Uniformities
Fuzzy Topology and Fuzzy Uniformity
Separation in Fuzzy Uniform Spaces
Fuzzy Uniform Spaces
Characterization of Fuzzy Uniform Spaces
REFERENCES
INDEX
