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Brouwer Fixed Point Theorem

Any continuous function G:B^n->B^n has a fixed point, where

B^n={x in R^n:x_1^2+...+x_n^2<=1}

is the unit n-ball.

See also

Ball, Fixed Point Theorem, Map Fixed Point

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References

Harvey Mudd College Mathematics Department. "Mudd Math Fun Facts: Brouwer Fixed Point Theorem." http://www.math.hmc.edu/funfacts/ffiles/20002.7.shtml.Kannai, Y. "An Elementary Proof of the No Retraction Theorem." Amer. Math. Monthly 88, 264-268, 1981.Milnor, J. W. Topology from the Differentiable Viewpoint. Princeton, NJ: Princeton University Press, p. 14, 1965.Munkres, J. R. Elements of Algebraic Topology. New York: Perseus Books Pub.,p. 117, 1993.Samelson, H. "On the Brouwer Fixed Point Theorem." Portugal. Math. 22, 189-191, 1963.

Referenced on Wolfram|Alpha

Brouwer Fixed Point Theorem

Cite this as:

Weisstein, Eric W. "Brouwer Fixed Point Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BrouwerFixedPointTheorem.html

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