Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Topology (Top)

Practical information
Study year 2016/2017
Block 2
Programme level Bachelor
Course responsible
  • Gijs Heuts (6-4c4d6a7a7978457266796d33707a336970)
  • Department of Mathematical Sciences
Course number: NMAA05010U

Course content

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
  • Retractions and fixed points


Secondary topics are:

  • Tychonoff Theorem
  • Compactifications
  • The fundamental group and 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


Recommended prerequisites

Analyse 2 (An2) or similar.

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BSc programme in Mathematics


Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)


Gijs Heuts


1 block


---- SKEMA LINK ----

Teaching and learning methods

5 hours of lectures and 3 hours of exercises per week for 7 weeks.


No limit




Category Hours
Lectures 45
Practical exercises 27
Preparation 131
Exam 3
English 206


Type of assessment

Continuous assessment
Written examination, 3 hour under invigilation
A complete evaluation of weekly work (weighted 50%) and a written 3 hour final exam with all aids (weighted 50%) constitute the basis for assessment.


All aids allowed

NB: If the exam is held at the ITX, the ITX will provide computers. Private computers, tablets or mobile phones CANNOT be brought along to the exam. Books and notes should be brought on paper or saved on a USB key.

Marking scale

7-point grading scale

Criteria for exam assessment

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

Censorship form

No external censorship
One internal examiner


Re-exam: Consists of two parts both weighted 50%:
1. A written assignment covering the breath of the course that must be handed in to the course responsible at the latest 2 days before the written exam (see 2).
2. A 3 hour written exam under invigilation. All aids allowed.

Mere information om kurset
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