18.S190 | January IAP 2023 | Undergraduate

Introduction to Metric Spaces


Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


18.100A Real Analysis

or 18.100P Real Analysis

Course Description

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.


Lebl, Jiri. Basic Analysis I: Introduction to Real Analysis, Volume 1. CreateSpace Independent Publishing Platform, 2018. ISBN: 9781718862401. This book is available as a free PDF download. You can purchase a paper copy by following a link at the same site.

Munkres, James R. Topology. Pearson, 2015. ISBN: 9789332549531.

Thomson, Brian S., Judith B. Bruckner, and Andrew M. Bruckner. Elementary Real Analysis. CreateSpace Independent Publishing Platform, 2008. ISBN: 9781434841612. This book is available as a free PDF download (PDF - 5.96 MB)


This class will be Pass/No Record with grading based on assignments and participation. There will be three problem sets, and there will not be any exams.


Lecture # and Topics Key Dates
Lecture 1: Motivation, Intuition, and Examples   
Lecture 2: General Theory Problem Set 1 due
Lecture 3: Compact Sets in Rⁿ  Problem Set 2 due
Lecture 4: Compact Metric Spaces   
Lecture 5: Complete Metric Spaces  Problem Set 3 due
Lecture 6: Where We Go from Here  

Course Info

As Taught In
January IAP 2023
Learning Resource Types
Lecture Notes
Lecture Videos
Online Textbook
Problem Sets
Instructor Insights