be a nondecreasing knot vector in $\mathbb{R}$. Set $a:=t_r$, $b:=t_{M-r}$, and $\mathcal{K}:=\{t_j:0\leq j\leq M\}$. For $0\leq i\leq M-1$, define the degree-zero B-spline $N_{i,0}:\mathbb{R}\to\mathbb{R}$ by
where every term with zero denominator is interpreted as the zero function. Then, for every $x\in [a,b]\setminus\mathcal{K}$, the active degree-$r$ B-splines satisfy