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Massachusetts Institute of Technology

Introduction to Metric Spaces

Massachusetts Institute of Technology via MIT OpenCourseWare

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Overview

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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

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

Taught by

Paige Bright

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