Student Co-author

HMC Undergraduate

Document Type

Article - preprint


Mathematics (HMC)

Publication Date



We define the infinite-dimensional simplex to be the closure of the convex hull of the standard basis vectors in R, 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.


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© 2007 Elsevier

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