Course teacher(s)
Andriy Haydys (Coordinator)ECTS credits
5
Language(s) of instruction
french
Course content
Metric spaces. Topological spaces. Hausdorff spaces. Connected spaces. Compactness via open covers. Compactness via sequences. Completeness. Criteria for compactness.
Objectives (and/or specific learning outcomes)
This course introduces metric and topological spaces. The aim is to formulate a language which is effective for discussing the continuity of a map between two spaces. The result is to give precise meaning to the slogan "f is continuous if a small change in x implies a small change in f(x)". Having seen the definition of a continuous map, we study the relation between the space itself and the behaviour of continuous maps into and out of the space. We discuss, amongst other topics, Hausdorff spaces, connected spaces and compact spaces.Ce cours introduit les espaces métriques et topologiques. L'objectif est de trouver un langage effectif pour discuter la continuité d'une application entre deux espaces. Le résultat est une précision du slogan "f est continue si un petit changement de x entraîne un petit changement de f(x)". Ayant vu la définition d'une application continue, nous étudions la relation entre l'espace soi-même et le comportement des applications continues de l'espace ou vers l'espace. Nous traitons, en particulier, les espaces de Hausdorff, les espaces compacts, les espaces connexes.
Prerequisites and Corequisites
Required and corequired courses
Courses requiring this course
Teaching methods and learning activities
Lectures and tutorials
References, bibliography, and recommended reading
Lecture notes available from the Université Virtuel. We will for the most part follow the book "An introduction to metric and topological spaces" by Wilson Sutherland.
Other information
Contacts
joel.fine@ulb.ac.be
Evaluation
Method(s) of evaluation
- Other
Other
3h written exam.
Language(s) of evaluation
- french