MAT3500 - Topology

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Course content

This course is an introduction to topological spaces. It deals with constructions like subspaces, product spaces, and quotient spaces, and properties like compactness and connectedness. The course concludes with an introduction to fundamental groups and covering spaces.

Learning outcome

After having completed the course:

• you can work with sets and functions, images and preimages, and you can distinguish between finite, countable, and uncountable sets

• you know how the topology on a space is determined by the collection of open sets, by the collection of closed sets, or by a basis of neighbourhoods at each point, and you know what it means for a function to be continuous

• you know the definition and basic properties of connected spaces, path connected spaces, compact spaces, and locally compact spaces

• you know what it means for a metric space to be complete, and you can characterise compact metric spaces

• you are familiar with the Urysohn lemma and the Tietze extension theorem, and you can characterise metrizable spaces

• you are familiar with the construction of the fundamental group of a topological space and applications to covering spaces and homotopy theory

Admission

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.

Prerequisites

Formal prerequisite knowledge

In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:

• Mathematics R1 (or Mathematics S1 and S2) + R2

And and in addition one of these:

• Physics (1+2)
• Chemistry (1+2)
• Biology (1+2)
• Information technology (1+2)
• Geosciences (1+2)
• Technology and theories of research (1+2)

The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies (in Norwegian).

Recommended previous knowledge

MAT1100 - Calculus, MAT1110 - Calculus and linear algebra, MAT1120 - Linear algebra, MAT2400 - Real Analysis. It will be useful to have taken MAT2200 - Groups, Rings and Fields.

Overlapping courses

10 credits overlap with MAT4500 - Topology

9 credits with MA232, 10 credits with MA245, 9 credits with MA144 and 6 credits with MA140.

*The information about overlaps is not complete. Contact the Department for more information if necessary.

Teaching

6 hours of lectures/exercises per week throughout the semester.

Examination

One compulsory assignment has to be handed in and approved. Final mark based on written examination at the end of the semester.

Rules for compulsory assignments at the Department of Mathematics.

Examination support material

No examination support material is allowed.

Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Resit an examination

This course offers both postponed and resit of examination. Read more:

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course

10

Bachelor

Every autumn

Every autumn

Teaching language

English

The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian.

Contact

Department of Mathematics