MAT4500 – Topology

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.

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.

• MAT1100 – Calculus
• MAT1110 – Calculus and Linear Algebra
• MAT1120 – Linear Algebra / MAT1125 – Advanced linear algebra
• MAT2400 – Real Analysis
• It will also be an advantage to have taken the following courses:
  • MAT2200 – Groups, Rings and Fields

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.

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

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass, the original examination.