Aims and Fit of Module

Metric spaces are sets equipped with a notion of distance. This module examines how important ideas and concepts of real analysis can be extended to the more general setting of metric spaces. 


This module provides a foundation for further study in a wide range of mathematical topics, including analysis, topology, measure theory, geometry and dynamical systems.

Learning outcomes

A	Recognise whether a given structure forms a metric space.

B	Work effectively with subsets of a metric space and determine the diameter, boundary, interior or closure.

C	Prove results concerning continuous maps between metric spaces.

D	Demonstrate whether or not a given metric space is connected, compact or complete.

E	Use the Banach contraction mapping theorem to identify fixed points.

F	Solve mathematical problems using the formalism of metric spaces.

Method of teaching and learning

This module will be delivered mainly through a combination of formal lectures and tutorials.