View source for Brouwer's fixed-point theorem

'''Brouwer's fixed-point theorem''' states that any continuous function mapping a compact convex set into itself has at least one fixed point — a point that the function maps to itself. Proved by [[L. E. J. Brouwer]] in 1910, before his foundational revolution in intuitionism, the theorem is one of the cornerstones of algebraic topology. It has profound applications in economics (proving the existence of [[General equilibrium theory|general economic equilibrium]]), game theory (the existence of Nash equilibria), and differential equations. The theorem is non-constructive: it guarantees the existence of a fixed point without providing a method for finding it, a feature that makes it controversial from a [[Constructivism|constructivist]] perspective and connects the theorem to deeper questions about the meaning of existence proofs in mathematics.

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[[Category:Topology]]
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