A fixed point theorem for the infinite-dimensional simplex
| dc.creator | Rizzolo, Douglas | |
| dc.creator | Su, Francis Edward | |
| dc.date | 2006-10-24 | |
| dc.date.accessioned | 2026-07-07T08:25:58Z | |
| dc.date.available | 2026-07-07T08:25:58Z | |
| dc.description | 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. | |
| dc.description | 8 pages; related work at http://www.math.hmc.edu/~su/papers.html | |
| dc.identifier | https://arxiv.org/abs/math/0610707 | |
| dc.identifier | http://arxiv.org/abs/math/0610707 | |
| dc.identifier | J. Math. Anal. Appl. 332 (2007) 1063-1070 | |
| dc.identifier | doi:10.1016/j.jmaa.2006.10.077 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136796 | |
| dc.subject | General Topology | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Combinatorics | |
| dc.subject | 54H25 (Primary); 47H10, 55M20 (Secondary) | |
| dc.title | A fixed point theorem for the infinite-dimensional simplex | |
| dc.type | text |