Let \(f:D^2\to D^2\) be a homeomorphism, where \(D^2\) is the closed unit disk in \(\mathbb R^2\). Show that every boundary point \(x\in\partial D^2\) satisfies \[ f(x)\in\partial D^2. \]
A homeomorphism of the closed disk preserves its boundary
P-TOP-WORKSHOP-QPH-04
- Area
- Topology
- Topics
- Homeomorphisms, Manifolds
- Status
- draft