Definition: A function $f:{\mathbb{R}}^d\to \mathbb{R}$ is called uniformly continuous if for all $ϵ>0$, there exists $\delta >0$ such that for all $\mathbf{x},\mathbf{y}\in {\mathbb{R}}^d:\Vert \mathbf{x}-\mathbf{y}\Vert <\delta$, we have $|f(\mathbf{x})-f(\mathbf{y})|<ϵ$.