Metric and topological spaces

[kbuzzard]

This is the optional 2nd year course. Metric spaces and topological spaces are in mathlib so let's check out their interfaces and see how good they are. We could start by digitising some of the example sheet questions or the theorems of the course. Let's start with the statements of the theorems and worry about proofs later.

[kbuzzard]

Let's do the contraction mapping theorem, for example!

[kbuzzard]

@rmitta is working through some of Sutherland. @SG4316 is thinking about connected spaces. @lgerolla is trying to do some alg top -- fundamental groups -- this is M3P21. He's using Hatcher. @GUILLERMOBAY is thinking about compact things.