MATH-220 / 5 crédits

Enseignant: Aru Juhan

Langue: Anglais


Summary

In metric spaces a distance is defined between each pair of points. In topological spaces, distances are replaced by only a certain notion of nearness. This abstract setting sheds new light upon basic questions: What is continuity? When should we consider two spaces to be equal?

Content

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 topological spaces and their properties
  • Analyze topological structures
  • Prove basic results in the language of topology

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

Notes/Handbook

There are written notes for the course.

Prerequisite for

Topology; advanced courses in analysis and geometry.

Dans les plans d'études

  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Metric and topological spaces
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11 ELA1CE1105
MAA112
MAA110
  
11-12   
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     

Mardi, 10h - 12h: Cours ELA1

Mercredi, 10h - 12h: Exercice, TP CE1105
MAA112
MAA110