# 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

## Prerequisite for

Topology; advanced courses in analysis and geometry.

## In the programs

**Semester:**Fall**Exam form:**Written (winter session)**Subject examined:**Metric and topological spaces**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks