Due November 9
The fixed points of a continuous might not be interior.
The Brouwer fixed point theorem is false for the open ball.
Let be compact and convex, and continuous. Then f has a fixed point.
Let be compact and convex with boundary, , and given by the intersection point of the line from to , on the side of . Then .
Note that, if is an interior point of , then is a retraction from onto .