This unit will cover algebraic topology, following on from MAS331: Metric Spaces. Topology studies the shape of space, with examples such as spheres, the Mobius Band, the Klein bottle, the torus and ...

It combines Barr's relational presentation of topological spaces in terms of ultrafilter convergence with Lawvere's interpretation of metric spaces as small categories enriched over the extended real ...

it introduces topology thoroughly from scratch and assumes minimal basic knowledge of real analysis and metric spaces. It begins with thought-provoking questions to encourage students to learn about ...