Fuzzy Topology

Preface

vii

Chapter 1. Preliminaries

(31)

1.1 Sets and Lattices

(11)

1.2 Operations on Lattices

(13)

1.3 Characterizations of Complete Distributivity

(7)

Chapter 2. Fuzzy Topological Spaces

(28)

2.1 Fuzzy Sets and Mappings

(8)

2.2 Fuzzy Topological Spaces

(6)

2.3 Multiple Choice Principle and Neighborhood Structure

(11)

2.4 Continuous Mappings

(3)

Chapter 3. Operations on Fuzzy Topological Spaces

(13)

3.1 Subspaces

(5)

3.2 Product Spaces

(5)

3.3 Sum Spaces

(1)

3.4 Quotient Spaces

(2)

Chapter 4. L-valued Stratification Spaces

(21)

4.1 Stratified Spaces and Stratifizations

(2)

4.2 Weakly Induced Spaces

(5)

4.3 Induced Spaces

(9)

4.4 Functors w(L) and t(L)

(3)

4.5 Analytic and Topological Characterizations of Completely Distributive Law

(2)

Chapter 5. Convergence Theory

(22)

5.1 Net Convergence Theory

(8)

5.2 Filter Convergence Theory

102

(9)

5.3 Convergence Classes

111

(5)

Chapter 6. Connectedness

116

(8)

6.1 Connectedness

116

(6)

6.2 Connectedness of L-valued Stratification Spaces

122

(2)

Chapter 7. Some Properties Related to Cardinals

124

(10)

7.1 Weight, Characteristic and Density

124

(5)

7.2 Countability

129

(1)

7.3 On L-valued Weakly Induced Spaces

130

(4)

Chapter 8. Separation (I)

134

(17)

8.1 Quasi-T(o)-, Sub-T(o)-, T(o)-, and T1-separations

134

(5)

8.2 T(2)-separation

139

(6)

8.3 Regularity

145

(6)

Chapter 9. Separation (II)

151

(36)

9.1 L-fuzzy Unit Interval -- I(L) and I(L)

151

(10)

9.2 Complete Regularity, Normality and Embedding Theory

161

(20)

9.3 Insertion Theorem

181

(6)

Chapter 10. Compactness

187

(23)

10.1 Some Kinds of Compactness in Fuzzy Topological Spaces

187

(2)

10.2 N-compactness

189

(6)

10.3 Tychonoff Product Theorem

195

(5)

10.4 Comparison of Different Compactness in Fuzzy Topological Spaces

200

(10)

Chapter 11. Compactification

210

(12)

11.1 Basic Theory of Compactification

210

(8)

11.2 Stone-Cech Compactification

218

(4)

Chapter 12. Paracompactness

222

(25)

12.1 Local Finiteness and Flinty Finiteness

222

(4)

12.2 Paracompactness and Flinty Paracompactness

226

(16)

12.3 Separations, Lindel of Property and Paracompactness

242

(5)

Chapter 13. Uniformity and Proximity

247

(38)

13.1 Uniformity

247

(30)

13.2 Proximity

277

(8)

Chapter 14. Metric Spaces

285

(23)

14.1 Metrics in Hutton's Sense and Erceg's Sense

285

(6)

14.2 Pointwise Characterizations of Metrics

291

(5)

14.3 Metrization

296

(12)

Chapter 15. Relations between Fuzzy Topological Spaces and Locales

308

(19)

15.1 Related Results in Locales

308

(6)

15.2 Separations in Fuzzy Topological Spaces and Locales

314

(1)

15.3 Relations between Fuzzy Topological Spaces and Locales

315

(5)

15.4 Fuzzy Stone Representation Theorem

320

(7)

Bibliography

327

(10)

Index

337

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