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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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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. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| None. A good knowledge of topological concepts (open sets connectedness compactness) in the Euclidean space Rn is useful. |
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Mode of delivery (face-to-face ; distance-learning) :
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| Face-to-face
The course and evaluation will be scheduled by the department of mathematics. |
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Recommended or required readings :
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| The lecture notes of Professor M. De Wilde will be available from the first lesson. |
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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 one of the themes that were dealt with in the theoretical course or that they read in the literature.
Reports given by the students may be taken into account. |
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Contacts :
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| Fabian Radoux
Department of mathematics, Grande Traverse,12, B37 4000 Liège Belgium
Phone : +32(0)4/366.94.80
Email : P.Mathonet@ulg.ac.be |
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| Items online : |
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| Lecture notes in general topology |
| These notes are the lecture notes of the course of general topology given in the third year of the Bachelor in Mathematical Sciences |
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