#### Description

This is an introduction to topology for qualified undergraduates.

#### Prerequisites

MATH 410

#### Topics

Metric spaces, topological spaces

Continuous maps and homeomorphisms

Connectedness, compactness (including Heine-Borel, Bolzano-Weierstrass, Ascoli-Arzela theorems),

Cantor sets

Fundamental group (homotopy, covering spaces, the fundamental theorem of algebra, Brouwer fixed point theorem)

Surfaces (e.g., Euler characteristic, the index of a vector field, hairy sphere theorem)

Elements of combinatorial topology (graphs and trees, planarity, coloring problems)