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Pure metric geometry: introductory lectures

Anton Petrunin

Abstract

We discuss domestic affairs of metric spaces, keeping away from any extra structure. Topics include universal spaces, injective spaces, Hausdorff and Gromov--Hausdorff convergences, and ultralimits.

Pure metric geometry: introductory lectures

Abstract

We discuss domestic affairs of metric spaces, keeping away from any extra structure. Topics include universal spaces, injective spaces, Hausdorff and Gromov--Hausdorff convergences, and ultralimits.

Paper Structure

This paper contains 49 sections, 265 equations, 11 figures.

Table of Contents

  1. Definitions
  2. Metric spaces
  3. Topology
  4. Variations
  5. Maximal metric and gluing
  6. Completeness
  7. G-delta sets
  8. Compact spaces
  9. Proper spaces
  10. Geodesics
  11. Metric trees
  12. Length
  13. Length spaces
  14. Universal spaces
  15. Embedding in a normed space
  16. ...and 34 more sections

Figures (11)

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  • ...and 6 more figures