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
| Office hours | No |
| Assistants | Yes |
| Forum | Yes |
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
Prerequisite for
Topology (Math-225). Advanced courses in analysis and geometry.
In the programs
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Topology I - point set topology
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: mandatory