Two decades of fuzzy topology: basic ideas, notions, and results

Abstract

CONTENTS Introduction § 0. Preliminaries: fuzzy sets § 1. Fuzzy topological spaces: the basic categories of fuzzy topology § 2. Fundamental interrelations between the category Top of topological spaces and the categories of fuzzy topology § 3. Local structure of fuzzy topological spaces § 4. Convergence structures in fuzzy spaces § 5. Separation in fuzzy spaces § 6. Normality and complete regularity type properties in fuzzy topology § 7. Compactness in fuzzy topology § 8. Connectedness in fuzzy spaces § 9. Fuzzy metric spaces and metrization of fuzzy spaces § 10. The fuzzy real line and its subspaces § 11. Fuzzy modification of a linearly ordered space § 12. Fuzzy probabilistic modification of a topological space § 13. The interval fuzzy real line § 14. On hyperspaces of fuzzy sets § 15. Another view of the subject of fuzzy topology and certain categorical aspects of it Conclusion: some reflections on the role and significance of fuzzy topology References