Metric and topological spaces

Summary

A topological space is a space endowed with a notion of nearness. A metric space is an example of a topological space, where the concept of nearness is measured by a distance function. Within this abstract setting we can ask: What is continuity? When are two topological/metric spaces equal?

Learning Prerequisites

Required courses

First year courses in the Bloc "Sciences de base" in EPFL Mathematics Bachelor's program;

Learning Outcomes

By the end of the course, the student must be able to:

• Define what is a topological/metric space as well as their properties
• Describe a range of important examples of topological and metric spaces
• Analyze topological/metric structures
• Prove basic results about topological/metric structures

Teaching methods

Lectures and exercise classes.

Assessment methods

written exam

Supervision

Office hours	No
Assistants	Yes
Forum	No

Resources

Bibliography

There are many good books on general topology. For example, here are a few that are available also at the EPFL library:

 

Introduction to topology, by T. Gamelin et R. Greene;

Topology, Second Edition, by J. Munkres;

Introduction to metric and topological spaces, by W. A. Sutherland

Ressources en bibliothèque

• Topology /Munkres
• Introduction to topology /Gamelin & Greene
• Introduction to metric and topological spaces / Sutherland

Notes/Handbook

There are written notes for the course.

Moodle Link

• https://go.epfl.ch/MATH-220

Prerequisite for

Topology; advanced courses in analysis and geometry.