This statement can be proved by using the fact that the game of hex cannot end in a draw.
This statement can be proved by using the fact that the game of hex cannot end in a draw. This statement, which is equivalent to the Knaster-Kuratowski- Mazurkiewicz lemma, has a generalized version named for Schauder. This result is used in the proof of the Borsk-Ulam theorem. This result stemmed from a novel proof of the   hairy ball theorem using homotopy, and its  rst proof relied on the notion of degree. This statement is equivalent to a statement about labeling the edges of triangles called Sperner's Lemma. For ten points, identify this theorem stating that any continuous map from a closed ball to itself must map at least one point to itself.
This statement can be proved by using the fact that the game of hex cannot end in a draw.
Brouwer  fixed point theorem [prompt on  xed point theorem]