Topology

Overview

- Definition and examples (natural, geometric and pathological)
- Continuity and homeomorphisms
- Compact, Connected, Hausdorff
- Subspaces and product spaces
- Introduction to homotopy, calculations and applications

Learning Objectives

It is intended that students shall, on successful completion of this module, be able to: use effectively the notions of topological space, continuous function and homeomorphism and give examples thereof; state and use the basic properties of the product and subspace topologies; apply effectively the properties of connectedness, compactness, and Hausdorffness; understand the relation between metric and topological spaces; understand how topological maps are related via homotopy and apply homotopical calculations to examples.

Skills

Analytic argument skills, problem solving, analysis and construction of proofs.

Assessment

None