# Topology

## Overview

This course is an introduction to topology and algebraic topology. First we will introduction fundamental concepts such as topological spaces, continuity and homomorphisms, as well as constructions like subspaces and quotient spaces. We will also discuss connectedness, compactness (including the theorem of Tychonoff) and separation axioms (the theorem of Urysohn-Tietze).

Often invariants, for example the number of connected components are used to study topological spaces. Algebraic topology is the study and construction of such invariants. We will define concepts such as homotopy and will introduce the fundamental group as the first such invariant. The fundamental group classified loops up to homotopy in a topological space and by the end of the lecture series we will see that the fundamental group also determines the behaviour of so-called covering spaces of the space.

## Registration

This course will be held online. If you are interested in attending, please sign up for the course by sending an email to

Dr. Viktor Kleen