Course content

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.

Learning outcome

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 characterize compact metric spaces

  • are familiar with the Urysohn lemma and the Tietze extension theorem, and you can characterize 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.

Admission to the course

Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.

Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

Overlapping courses

  • 10 credits overlap with MAT3500 – Topology.
  • 10 credits overlap with MA245.
  • 9 credits overlap with MA232.
  • 9 credits overlap with MA232.
  • 9 credits overlap with MA144.
  • 6 credits overlap with MA140.


6 hours of lectures/exercises per week throughout the semester.

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.


Final written exam which counts 100 % towards the final grade. 

This course has 1 mandatory assignment that must be approved before you can sit the final exam. The mandatory assignment must be written with a typesetting software for writing mathematics (e.g. LaTeX).

It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT3500 – Topology

Examination support material

No examination support material is allowed.

Language of examination

Courses taught in English will only offer the exam paper in English. You may submit your response in Norwegian, Swedish, Danish or English.

Grading scale

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.

Resit an examination

This course offers both postponed and resit of examination. Read more:

Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Dec. 6, 2022 7:35:11 AM

Facts about this course

Teaching language