  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 $\Gamma : [0,1] \to \R^n$ and for any
positive integer N, there exist points $t_0=0<t_1<...<t_{N-1}<1=t_N$, such that
$d(\Gamma(t_{i-1}),\Gamma(t_i))=d(\Gamma(t_{i}),\Gamma(t_{i+1}))$ 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.
