Topology I - point set topology

Summary

A topological space is a space endowed with a notion of nearness. A metric space is an example of a topological space, where a distance function measures the concept of nearness. 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 block "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 a topological space is as well as their properties.
• Describe a range of important examples of topological and metric spaces.
• Analyze topological and metric structures.
• Prove basice results about topological and metric structures.

Teaching methods

Lectures and exercise classes.

Assessment methods

One final written exam.

Supervision

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.

Notes/Handbook

There are written notes for the course.

Moodle Link

• https://go.epfl.ch/MATH-220

Prerequisite for

Topology (Math-225). Advanced courses in analysis and geometry.