# Topology (Top)

### 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

Secondary topics are:

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

BSc Programme in Mathematics

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

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

Lebesgueintegralet og målteori (LIM) - alternatively Analyse 2 (An2) from previous years or similar

Written
Oral
Individual
Continuous feedback during the course of the semester
ECTS
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
Censorship form
No external censorship
One internal examiner
##### Criteria for exam assessment

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

Single subject courses (day)

• Category
• Hours
• Lectures
• 35
• Preparation
• 147
• Theory exercises
• 21
• Exam
• 3
• English
• 206