A fixed point theorem for the infinite-dimensional simplex

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We define the infinite dimensional simplex to be the closure of the convex hull of the standard basis vectors in R^infinity, and prove that this space has the 'fixed point property': any continuous function from the space into itself has a fixed point. Our proof is constructive, in the sense that it can be used to find an approximate fixed point; the proof relies on elementary analysis and Sperner's lemma. The fixed point theorem is shown to imply Schauder's fixed point theorem on infinite-dimensional compact convex subsets of normed spaces.
8 pages; related work at http://www.math.hmc.edu/~su/papers.html

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General Topology, Classical Analysis and ODEs, Combinatorics, 54H25 (Primary); 47H10, 55M20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/136796

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610707
 http://arxiv.org/abs/math/0610707
 J. Math. Anal. Appl. 332 (2007) 1063-1070
 doi:10.1016/j.jmaa.2006.10.077

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arXiv