A Combinatorial Approach to the Brouwer Fixed Point Theorem
نویسنده
چکیده
The Brouwer Fixed Point Theorem states that any continuous mapping from a closed ball in Euclidean space to itself has at least one fixed point. This theorem has a wide variety of applications in areas such as differential equations, economics, and game theory. Although this is fundamentally an analytic and topological statement, there exists an elegant combinatorial proof using Sperner’s Lemma. We take the combinatorial approach of [3] for the oneand two-dimensional cases, then synthesize the methods of [1] and [2] for the general case.
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