NMAA05010U Topology (Top)

Volume 2021/2022

BSc Programme in Mathematics


This is a course on topological spaces and continuous maps. Main topics of this course are:

  • Topological Spaces
  • Subspace, Order, Product, Metric and Quotient Topologies
  • Continuous Functions
  • Connectedness and Compactness
  • Countability and Separation Axioms


Secondary topics are:

  • Retractions and fixed points
  • Tychonoff Theorem
  • Compactifications
  • Vistas of algebraic topology
Learning Outcome

This course will enable the participants to work with basic topological concepts and methods.  At the end of the course, the students are expected to have attained:


  • understand and assimluate the concepts and methods of the main course topics including basic definitions and theorems
  • understand secondary topics covered in the specific course



  • determine properties of a topological space such as Hausdorffness, countability, (path) connectedness, (local) compactness
  • construct new spaces as subspaces, quotient spaces and product spaces of known ones



  • analyze concrete topological spaces using acquired knowledge and skills
  • relate the theory of topological spaces and continuous maps to specific settings in past and future math courses


Lebesgueintegralet og målteori (LIM) - alternatively Analyse 2 (An2) from previous years or similar
5 hours of lectures and 3 hours of exercises per week for 7 weeks.
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 147
  • Theory exercises
  • 21
  • Exam
  • 3
  • Total
  • 206
Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Continuous assessment
Written examination, 3 hour under invigilation
A complete evaluation of weekly work (weighted 50%) and a written 3 hour ‘closed-book’ final exam (weighted 50%) constitute the basis for assessment.
Only certain aids allowed

All aids allowed for the weekly homework. No books and no electronic aids are allowed for the 3 hours final exam. Personally created handwritten notes on paper are allowed.

Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner

Consists of a 3 hour written exam under invigilation (weighted 50%).
Only certain aids allowed: No books and no electronic aids are allowed. Personally created handwritten notes on paper are allowed.
For the weekly homework (weighted 50%), students can choose to keep the results from their course work or to participate in a 30 minutes oral examination of the weekly homework, in which case the score from the oral examination will count as the homework

Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.