MAT4500 – Topology
Course description
Schedule, syllabus and examination date
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 completing the course you
can work with sets and functions, images and preimages, and you can distinguish between finite, countable, and uncountable sets
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
know the definition and basic properties of connected spaces, path connected spaces, compact spaces, and locally compact spaces
know what it means for a metric space to be complete, and you can characterize compact metric spaces
are familiar with the Urysohn lemma and the Tietze extension theorem, and you can characterize metrizable spaces
are familiar with the construction of the fundamental group of a topological space
master LaTeX as an electronic tool for writing mathematics.
Admission to the course
Students admitted at UiO must?apply for courses?in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.
Nordic citizens and applicants residing in the Nordic countries may?apply to take this course as a single course student.
If you are not already enrolled as a student at UiO, please see our information about?admission requirements and procedures for international applicants.
Recommended previous knowledge
- MAT1100 – Calculus
- MAT1110 – Calculus and Linear Algebra
- MAT1120 – Linear Algebra
- MAT2400 – Real Analysis
- It will also be an advantage to have taken the following courses:
Overlapping courses
- 10 credits overlap with MAT3500 – Topology.
- 10 credits overlap with MA245.
- 9 credits overlap with MA232.
- 9 credits overlap with MA232.
- 9 credits overlap with MA144.
- 6 credits overlap with MA140.
Teaching
6 hours of lectures/exercises per week throughout the semester.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Examination
Final written exam which counts 100 % towards the final grade.?
This course has 1 mandatory assignment that must be approved before you can sit the final exam. The mandatory assignment must be written with a typesetting software for writing mathematics (e.g. LaTeX).
It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT3500 – Topology
Examination support material
No examination support material is allowed.
Language of examination
Courses taught in English will only offer the exam paper in English. You may submit your response 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:
More about examinations at UiO
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.