MAT4500 – Topology
Schedule, syllabus and examination date
This course is an introduction to topological spaces. It deals with constructions like subspaces, product spaces, and quotient spaces, and properties like compactness and connectedness. The course concludes with an introduction to fundamental groups and covering spaces.
After completing the course you:
can work with sets and functions, images and preimages, and you can distinguish between finite, countable, and uncountable sets;
know how the topology on a space is determined by the collection of open sets, by the collection of closed sets, or by a basis of neighbourhoods at each point, and you know what it means for a function to be continuous;
know the definition and basic properties of connected spaces, path connected spaces, compact spaces, and locally compact spaces;
know what it means for a metric space to be complete, and you can characterise compact metric spaces;
are familiar with the Urysohn lemma and the Tietze extension theorem, and you can characterise metrizable spaces;
are familiar with the construction of the fundamental group of a topological space and applications to covering spaces and homotopy theory;
master LaTeX as an electronic tool for writing mathematics.
Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.
Recommended previous knowledge
10 credits overlap with MAT3500 – Topology
*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department.
6 hours of lectures/exercises per week throughout the semester.
1 mandatory assignment that has to be approved to attend the exam. The mandatory assignment must be written in LaTeX, a typesetting software for academic writing in mathematics.
Final written examination.
Examination support material
No examination support material is allowed.
Language of examination
Subjects taught in English will only offer the exam paper in English.
You may write your examination paper in Norwegian, Swedish, Danish or English.
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.
Explanations and appeals
Resit an examination
This course offers both postponed and resit of examination. Read more:
Withdrawal from an examination
It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.
Special examination arrangements
Application form, deadline and requirements for special examination arrangements.
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.