The planar <Brouwer fixed-point theorem> states that every continuous map from a nonempty <compact> convex subset of $\mathbb R^2$ to itself has a <fixed point>. In particular it applies to a closed disk or a closed triangle. Convexity and compactness are essential hypotheses in this formulation.

Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / ii / Paper 2 / 11F / a / Solution

 Solution (source code)