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