Metric Spaces

Overview

- definition and examples of metric spaces (including function spaces)
- open sets, closed sets, closure points, sequential convergence, density, separability
- continuous mappings between metric spaces
- completeness

Learning Objectives

It is intended that students shall, on successful completion of the module, be able to: understand the concept of a metric space; understand convergence of sequences in metric spaces; understand continuous mappings between metric spaces; understand the concepts and simple properties of special subsets of metric spaces (such as open, closed and compact); understand the concept of Hilbert spaces, along with the basic geometry of Hilbert spaces, orthogonal decomposition and orthonormal basis.

Skills

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

Assessment

None