NMAA05010U Topology (Top)

Volume 2026/2027
Education

BSc Programme in Mathematics

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

 

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:


Knowledge:

  • 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

 

Skills:

  • 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

 

Competences:

  • 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

 

Analyse 1 (An1)
5 hours of lectures and 4 hours of exercises per week for 7 weeks.
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 141
  • Theory exercises
  • 28
  • Exam
  • 2
  • Total
  • 206
Written
Oral
Individual
Continuous feedback during the course of the semester
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Type of assessment details
Two sets of homework problems and a final 2,5 hour written in-class test in week 9
of the course. The homework contributes 30% and the final test contributes 70% towards the final grade.
Aid
Only certain aids allowed (see description below)

Homework assignments: All aids allowed.

For the final written in class test: Handwritten notes and the (printed) lecture notes are allowed.

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

Consists of 2 elements:

  1. A 2,5 hour written in-class
    test. Same requirements as for the ordinary exam. Only
    certain aids allowed: handwritten notes and the (printed)
    lecture notes; no electronic devices. A 15 min oral
    examination (without preparation time) of the homework
    sets (weighted 30%). Students can choose to keep the
  2. results from their course work in which case they only
    participate in the written test, or they can participate in the
    15 minutes oral examination, in which case the score from
    the oral examination will count as the homework. If
    fewer than 10 people are signed up for the re-exam, the 2,5
    hour written test will be replaced by a 25 min oral
    examination (without preparation). In this case, students
    who choose not to keep the results from their homework,
    will participate in a 40 minutes oral examination of which 25
    minutes substitute for the written test, and 15 minutes are
    the examination of the 2 homework sets. The weights are
    30% for homework and 70% for the oral exam substituting
    the written test.
Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.