This is a lecture from Dr Feinstein's 4th-year module G14FUN Functional Analysis.

See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/ and, in particular, the associated blog post at http://wp.me/posHB-7y In this screencast, Dr Feinstein proves the Baire Category Theorem for complete metric spaces - a countable intersection of dense, open subsets of a complete metric space must be dense.

This material is suitable for those with a knowledge of metric space topology and, in particular, dense subsets and complete metrics.