A note on equipartition
| dc.creator | Lopez, M. A. | |
| dc.creator | Reisner, S. | |
| dc.date | 2007-07-29 | |
| dc.date | 2008-07-15 | |
| dc.date.accessioned | 2026-07-07T09:49:55Z | |
| dc.date.available | 2026-07-07T09:49:55Z | |
| dc.description | The problem of the existence of an equi-partition of a curve in $\R^n$ has recently been raised in the context of computational geometry. The problem is to show that for a (continuous) curve $Γ: [0,1] \to \R^n$ and for any positive integer N, there exist points $t_0=0<t_1<...<t_{N-1}<1=t_N$, such that $d(Γ(t_{i-1}),Γ(t_i))=d(Γ(t_{i}),Γ(t_{i+1}))$ for all $i=1,...,N$, where d is a metric or even a semi-metric (a weaker notion) on $\R^n$. We show here that the existence of such points, in a broader context, is a consequence of Brower's fixed point theorem. | |
| dc.description | Some misprints in earlier versions are corrected, one reference is added with remarks concerning it | |
| dc.identifier | https://arxiv.org/abs/0707.4298 | |
| dc.identifier | http://arxiv.org/abs/0707.4298 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164771 | |
| dc.subject | Computational Geometry | |
| dc.subject | Functional Analysis | |
| dc.subject | I.3.5 | |
| dc.title | A note on equipartition | |
| dc.type | text |