# NMAA05010U  Topology (Top)

Volume 2015/2016
Education

BSc programme in Mathematics
BSc programme in Natural Sciences and It

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:

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.
Lectures and single and/or group activities with consulting for 7 weeks,
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Written examination, 3 hour under invigilation
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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.
Aid
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
Censorship form
No external censorship
One internal examiner
Re-exam

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.

##### Criteria for exam assesment

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

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