Duration
30h Th, 20h Pr, 10h Mon. WS
Number of credits
| Bachelor in mathematics | 6 crédits | |||
| Master in mathematics (120 ECTS) | 6 crédits | |||
| Master in mathematics (60 ECTS) | 6 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the second semester
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
This course is an introduction to general topology.
The main purpose of general topology is the abstract definition and study of concepts such as continuity of mappings, connectedness, compactness ...
These concepts are usually defined in the first course in analysis for Euclidean spaces. They will be generalized for arbitrary sets.
For instance, the following topics could be presented :
The general definition of a topology, neighborhoods of points, interior, closure and boundary of a set.
We will study the continuity of mappings and define the initial and final topologies.
We will deal with subspaces, product spaces and quotient spaces.
The notion of convergence, of filter, the axioms of separation.
The notions of compact spaces and connected spaces.
A few classical theorems will also be presented.
Properties of topological vector spaces.
Learning outcomes of the learning unit
At the end of the course, the students should be able to make a presentation of the theory or to use it in order to solve exercises
They should also be able to read the literature in order to make a report and a short talk about a topic proposed by the teacher.
This knowledge of general topology is useful for the students for lectures in advanced algebra, geometry and analysis.
Prerequisite knowledge and skills
A basic knowledge of naïve set theory, functions, Euclidean spaces and quotient spaces is assumed. A good knowledge of topological concepts (open sets connectedness compactness) in the Euclidean spaces is useful.
Planned learning activities and teaching methods
Ex cathedra classes, exercice sessions and a personal work.
Mode of delivery (face to face, distance learning, hybrid learning)
Blended learning
Recommended or required readings
Lecture notes are available on eCampus.
There are also many textbooks on general topology available in the library of mathematics (building B52).
Exam(s) in session
Any session
- In-person
written exam AND oral exam
Written work / report
Additional information:
A written examination of exercises will be organized.
There will also be an oral examination and the realization of a personal work.
Work placement(s)
Organizational remarks
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Contacts
Céline Esser
Email : Celine.Esser@uliege.be
Département de Mathématique,
Allée de la Découverte, 12, B37,
4000 Liège, Sart-Tilman.
Office 1/75