Author(s): R. Lowen
Publisher: Clarendon
Year: 1997
Title page
Preface
INTRODUCTION
1 APPROACH SPACES
1.1 DISTANCES
1.2 LIMIT OPERATORS
1.3 APPROACH SYSTEMS
1.4 GAUGES
1.5 TOWERS
1.6 HULL OPERATORS
1.7 REGULAR FUNCTION FRAMES
1.8 APPROACH SPACES
1.9 CONTRACTIONS
1.10 THE TOPOLOGICAL CONSTRUCT AP
2 TOPOLOGICAL APPROACH SPACES
2.1 TOPOLOGICAL APPROACH STRUCTURES
2.2 THE EMBEDDING OF TOP lN AP
2.3 BIREFLECTIVE BICOREFLECTIVE SUBCONSTRUCTS
3 METRIC APPROACH SPACES
3.1 METRIC APPROACH STRUCTURES
3.2 CONVERGENCE lN METRIC APPROACH SPACES
3.3 THE EMBEDDING OF pqMETOO lN AP
3.4 THE EPIREFLECTIVE HULL OF pqMETOO
4 UNIFORM APPROACH SPACES
4.1 THE EPIREFLECTIVE HULL OF pMEToo
4.2 CONVERGENCE lN UAP
4.3 CATEGORICAL ASPECTS
4.4 RELATIONSHIP WITH UNIFORM SPACES
5 CANONICAL EXAMPLES
5.1 SPACES OF MEASURES
5.2 FUNCTlON SPACES
5.3 HYPERSPACES
5.4 PROBABILISTIC METRIC SPACES
5.5 SPACES OF RANDOM VARIABLES
6 APPROACH PROPERTIES
6.1 COMPACTNESS
6.2 CONNECTEDNESS
6.3 COMPLETENESS
7 COMPLETION
7.1 CONSTRUCTION
7.2 EXAMPLE: FUNCTION SPACES
8 COMPACTIFICATION
8.1 CONSTRUCTION
8.2 EXAMPLE: THE CASE OF βN
APPENDIX A
A.l BASIC CATEGORICAL CONCEPTS
A.2 TOPOLOGICAL CONSTRUCTS
A.3 REFLECTIVE AND COREFLECTIVE SUBCONSTRUCTS
APPENDIX B
B.l METRIC SPACES
B.2 PROBABILISTIC METRIC SPACES
B.3 CONVERGENCE SPACES
B.4 QUASI-UNIFORM AND UNIFORM SPACES
B.5 PROXIMITY SPACES
BIBLIOGRAPHY
INDEX
