Let $n\in\mathbb{N}$, let $a<b$, let $X\subset C[a,b]$ be an $n$-dimensional Haar space, let $w:[a,b]\to(0,\infty)$ be continuous, and let $f\in C[a,b]$. An element $p\in X$ is the best weighted uniform approximant to $f$ if and only if there exist points
paragraph
admin
\begin{align*}
a\le x_0<\dots<x_n\le b
\end{align*}
latex_env
admin
and a sign $\sigma\in\{-1,1\}$ such that, with $E=\|f-p\|_{\infty,w}$,