Catalog

Introduction to Metric Spaces

Mathematics MIT CC BY-NC-SA 4.0 6 lectures

This course provides a basic introduction to metric spaces. It covers metrics, open and closed sets, continuous functions (in the topological sense), function spaces, completeness, and compactness.

Syllabus

  1. 1 Lecture 1: Motivation, Intuition, and Examples
  2. 2 Lecture 2: General Theory
  3. 3 Lecture 3: Compact Sets in Rⁿ
  4. 4 Lecture 4: Compact Metric Spaces
  5. 5 Lecture 5: Complete Metric Spaces
  6. 6 Lecture 6: Where We Go from Here

Course materials