The Hairy Ball Theorem

A short topology path to a famous fact: you can't comb a hairy ball flat. Open sets, continuity, and the Euler characteristic lead to the Hairy Ball Theorem.

Topics on this path

1. Topological Spaces & Open Sets
2. Continuity in Topological Spaces
3. Compactness
4. Euler Characteristic & Surface Classification
5. Hairy Ball Theorem