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, students will be able to present the theory covered in class or apply it in exercises.
They will be familiar with the basic concepts of general topology.
They will also need to independently understand a topic related to the theory taught in order to complete an assignment on a subject determined by the teacher.
These foundational skills in general topology will be valuable in the students' cursus, including algebra, differential geometry, and analysis, to name a few major areas of application.
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
The course consists of theoretical lessons at the blackboard or online, exercise 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:
The examination will include an oral part, a written part, and an individual project.
The written exam will focus on solving exercises related to the topics covered in the lectures and exercises sessions.
The oral exam will cover the taught theory and its immediate applications.
Details regarding the project will be provided during the theoretical class.
Work placement(s)
Organisational remarks and main changes to the course
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Contacts
Céline Esser (Celine.Esser@uliege.be)
Assistant : Pierre Stas (Pierre.Stas@uliege.be)