Starting from your favourite set of real numbers, how many new sets can you produce by taking closures and complements? In 1922 Kuratowski found a set from which 13 new sets can be obtained in this fashion and then showed that this is the largest possible solution. Versions of this result also hold in many other areas of mathematics such as the theory of binary relations, formal languages and algebra.

We examine Kuratowski's (quite elementary) proof and some of its many variants in both topology and elsewhere. The talk is aimed at a general audience and requires familiarity with only the most basic concepts of topology on the reals (such as open intervals, closed intervals, closure and interior).

Convenor: Simon Clarke.