Lecture notes

Lecture notes ver 2.4.2024: PDF

Disclaimer: The notes may be updated at multiple instances throughout the course.

Video material

Playlist: Youtube

(Personal recommendation: Watch at 1.5x or 2x speed for a better experience.)


See also the course Timeline to find out which chapters/videos are covered in each session.

Course Description

In this course, we embark on an adventure in the study of general topological spaces. Topology itself is a fundamental branch of mathematics with many applications among all disciplines. In this course we will start from its beginnings and go rigorously through the basic theory needed to understand more advanced concepts. Topological notions such as continuity, convergence, and compactness have a profound impact throughout mathematics, and in this course we will recognize how these concepts emerge from the simple building blocks of topology.

The main topics are:

  • Topological spaces
  • Continuity and convergence
  • Product topology
  • Compactness and Connectedness
  • Separation and countability axioms
  • Urysohn's lemma and metrization theorem
  • Quotient spaces, Homotopies, and more!

Senast redigerad: tisdag, 2 april 2024, 13:35