Semester | Mand. | Option | Filières |
BA3 | x |
Lecture | 2 weekly |
Exercises | 2 weekly |
Study plan | Semester | Mand. | Option | Filières |
Mathématiques 2020-21 | BA3 | x |
Cursus | Sem. | Type |
---|---|---|
Mathematics | BA3 | Obl. |
In this course we will study basic notions of point-set topology.
Topology is the minimal structure on a set of points that allows to define a notion of continuity. We will see how this minimal structure is nevertheless rich enough to build up several other geometric concepts like connectedness or compactness. In contrast, we will also discuss how adding a distance function and thereby turning a topological space into a metric space introduces additional concepts missing in topological spaces, like for example completeness or boundedness.
Our basic questions are very simple: how to describe a topological or metric space? When should we consider two such spaces equal, how can we tell when they are different?
Roughly, the course will be in 4 chapters.
1) Topological spaces & continuity
2) Connectedness
3) Compactness
4) Metric spaces and completeness
Throughout the course we will discuss many examples, both to motivate and better understand the somewhat abstract notions.
First year courses in the Bloc "Sciences de base" in EPFL Mathematics Bachelor's program;
Lectures and exercise classes.
written exam
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
There are written notes for the course.
Topology; advanced courses in analysis and geometry.
obligatoire
obligatoire
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
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