This is a lecture on the properties of open sets in finite-dimensional Euclidean space by Dr Joel Feinstein from his second-year module on Mathematical Analysis. This material is suitable for those who already know the definitions of open set and of the interior of a set in finite-dimensional Euclidean space.

In this session Dr Feinstein shows that finite unions and intersections of open sets are open, and then discusses infinite unions and intersections. It turns out that infinite unions of open sets are still open, but that infinite intersections of open sets need not be open any more.

See also Dr Feinstein's blog, Explaining Mathematics, http//explainingmaths.wordpress.com/