2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136796We 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.htmlGeneral TopologyClassical Analysis and ODEsCombinatorics54H25 (Primary); 47H10, 55M20 (Secondary)text