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| MATH0212-2 | General Topology
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| Duration : | 30h Th, 30h Pr |
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| Number of credits : |
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| Lecturer : | Pierre Mathonet |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the first semester, review in January |
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Course contents :
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| 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.
The following topics will 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, quotient spaces and actions of topological groups.
The axioms of separation will be studied.
The last sections will be devoted to the definitions and properties of compact spaces and connected spaces.
A few classical theorems will also be presented. |
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Learning outcomes of the course :
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| 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.
It should also help them to think of several difficult points they could have to teach in the secondary school. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| A basic knowledge of naïve set theory, functions, Euclidean spaces is assumed. A good knowledge of topological concepts (open sets connectedness compactness) in the Euclidean spaces is useful. |
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Planned learning activities and teaching methods :
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| The theory is given mainly on the blackboard and is illustrated by simple examples whenever it is possible. Students are encouraged to ask questions and to participate.
During the exercise sessions, students are asked to solve exercises under the supervision of the teacher, who also gives a solution. When possible, a list of exercises will be given a few days before the exercise session, so that the student can prepare the exercises before the session. |
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Mode of delivery (face-to-face ; distance-learning) :
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| Face-to-face
The schedule of the lectures is determined by the "conseil des études en mathématiques" and available on the website of the department of mathematics. |
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Recommended or required readings :
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| Lecture notes are available on my web page :
http://www.geodiff.ulg.ac.be
These lecture notes are available (upon request) at very low price.
Please contact D. Bartholomeus (office 0/28, building B37).
There are also many textbooks on general topology available in the library of mathematics (building B52). |
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Assessment methods and criteria :
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| A written examination of exercises will be organized.
There will also be an oral examination.
The students will be asked to develop two of the themes that were dealt with in the theoretical course.
A list of major questions for the exams will be available at the end of the lectures.
The final result will be an arithmetic mean of the results obtained by the students for the two parts of the exam. |
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Work placement(s) :
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Organizational remarks :
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| The exam should take place in January, as indicated above. However, this has to be confirmed by the "Conseil des études en Mathématiques". This council also determines the schedule of exams. |
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Contacts :
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| For theory and exercices, feel free to contact me by email (see below) to make an appointment or come to my office :
Pierre Mathonet
Email : P.Mathonet@ulg.ac.be
Phone : +32(0)4/366.94.80
Department of Mathematics,
Grande Traverse 12, B37,
4000 Liège Belgium
Office 0/27
You can also contact Mr. J. Raskin.
Office 0/56 (building B37). |
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| Items online : |
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| Lecture notes in general topology |
| Lecture notes are available on the web page : |
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