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 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]