Module Title
Metric Spaces

Module Level
Level 2

Module Credits
5.00

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.

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.

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