Bornologies and Lipschitz Analysis

Cover
Title Page
Copyright Page
Preface
Table of Contents
List of Symbols
Introduction
1. Background Material
2. Continuous Functions on Metric Spaces
3. Extension of Real-Valued Continuous Functions on Subsets of a Metric Space
4. The Lipschitz Norm for the Vector Space of Lipschitz Real-Valued Functions
5. Nets and Uniformities
6. Some Basic Bornologies
7. Total Boundedness Revisited and Bourbaki Boundedness
8. Locally Lipschitz Functions
9. Common Sets of Boundedness for Classes of Continuous Functions
10. Hejcman’s Theorem and its Analog for Totally Bounded Subsets
11. General Constructions
12. Properties of Bornologies
13. Approximation by Members of a Bornology
14. Selected Topological Properties of the One-Point Extension
15. Bornologies of Metrically Bounded Sets
16. Bornologies of Totally Bounded Sets
17. Strong Uniform Continuity
18. UC-Subsets
19. UC-Spaces
20. Pointwise Products of Uniformly Continuous Real-Valued Functions
21. Strong Uniform Convergence on Bornologies
22. Uniform Convergence on Totally Bounded Subsets
23. Where Must Each Member of a Class of Locally Lipschitz Functions be Lipschitz?
24. Real-Valued Lipschitz Functions and Classes of Locally Lipschitz Functions
25. Metrically Convex Spaces and Coarse Maps
26. Some Density Results
27. More on our Four Classes of Locally Lipschitz Functions
28. Real-Valued Functionals and Bornologies
29. Uniformly Paracompact Subsets
30. Uniformly Paracompact Spaces and Uniformly Locally Lipschitz Functions
31. Bornological Convergence of Nets of Closed Subsets
32. Attouch-Wets Convergence
33. Topologies of Uniform Convergence on B(X, Y) and Convergence of Graphs
34. Bornological Convergence and Uniform Convergence of Distance Functionals
35. Bornological Convergence with Respect to the Compact Bornology
36. When is Bornological Convergence Topological?
37. Uniformizability and Metrizability
38. Ideals, Bornologies and Extensions
39. When is an Extension Bornological?
References
Index