Approach spaces : the missing link in the topology-uniformity-metric triad

書誌事項

Approach spaces : the missing link in the topology-uniformity-metric triad

R. Lowen

(Oxford mathematical monographs)

Clarendon Press, 1997

この図書・雑誌をさがす

注記

Includes bibliographical references and index

内容説明・目次

内容説明

In topology the three basic concepts of metrics, topologies and uniformities have been treated so far as separate entities by means of different methods and terminology. This is the first book to treat all three concepts as a special case of the concept of approach spaces. This theory provides an answer to natural questions in the interplay between topological and metric spaces by introducing a uniquely well suited supercategory of TOP and MET. The book explains the richness of approach structures in great detail; it provides a comprehensive explanation of the categorical set-up, develops the basic theory and provides many examples, displaying links with various areas of mathematics such as approximation theory, probability theory, analysis and hyperspace theory.

目次

  • Symbols
  • Preface
  • 1. Approach Spaces
  • 2. Topological Approach Spaces
  • 3. Metric Approach Spaces
  • 4. Uniform Approach Spaces
  • 5. Canonical Examples
  • 6. Approach Properties
  • 7. Completion
  • 8. Compactification
  • Appendix A
  • Appendix B
  • Index
  • Bibliography

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