NMAA05010U Topology (Top)

Volume 2018/2019
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
  • Retractions and fixed points

 

Secondary topics are:

  • 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 2 (An2) or similar.
5 hours of lectures and 3 hours of exercises per week for 7 weeks.
  • Category
  • Hours
  • Exam
  • 3
  • Lectures
  • 35
  • Practical exercises
  • 27
  • Preparation
  • 141
  • Total
  • 206
Credit
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.
Aid
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
Re-exam

Consists of a 3 hour written exam under invigilation. Only certain aids allowed: No books and no electronic aids are allowed. Personally created handwritten notes on paper are allowed.

Criteria for exam assesment

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