Sperner’s Lemma and Brouwer’s Fixed Point Theorem
نویسنده
چکیده
So Brouwer’s Fixed Point Theorem asserts that each Dn, n ≥ 1, is a fixed point domain. On the other hand, Dn less a point, [0, 1]∪ [2, 3] and R are not fixed point domains. (It is easy to construct appropriate functions with no fixed point for these sets.) The fact that Dn is compact is important in Brouwer’s Fixed Point Theorem. However, if G is a fixed point domain, and f : G → H is a continuous bijection with a continuous inverse, then H is a fixed point domain.
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