## Metric Spaces

Module Title Metric Spaces
Module Level Level 2
Module Credits 5.00

#### 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.
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#### 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.
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#### Method of teaching and learning

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

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