Aims

The objective is on one hand to initiate students to the notion of topological space and on the other hand to make them find short proofs of topological properties.
After this course they will be :
- familiar with a large series of topological spaces
- able to establish continuity/discontinuity of maps between topological spaces;
- able to recognize and to establish the compactness and connectedness of topological spaces and to draw conclusions;
- able to build and write short proofs concerning topological properties.

Main themes

Metric spaces
Topological spaces
Continuous maps .
Hausdorff spaces
Compact spaces
Connectedness

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Prerequisite : Mathematical analysis 3

Other credits in programs