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Brouwer Fixed Point Theorem

Any continuous Function $G:\Bbb{B}^n\to \Bbb{B}^n$ has a Fixed Point, where

\Bbb{B}^n=\{{\bf x}\in\Bbb{R}^n : {x_1}^2+\ldots+{x_n}^2\leq 1\}

is the unit $n$-Ball.

See also Ball, Fixed Point Theorem


Milnor, J. W. Topology from the Differentiable Viewpoint. Princeton, NJ: Princeton University Press, p. 14, 1965.

© 1996-9 Eric W. Weisstein