Definition:Computably Uniformly Continuous Real-Valued Function

Definition
Let $D \subseteq \R^n$ be a subset of real cartesian $n$-space.

Let $f : D \to \R$ be a real-valued function on $D$.

Suppose there exists a total recursive function $d : \N \to \N$ such that:
 * For every $n \in \N$ and $\bsx, \bsy \in D$ such that:
 * $\norm {\bsx - \bsy} < \dfrac 1 {\map d n + 1}$
 * where $\norm \cdot$ is the Euclidean norm, it holds that:
 * $\size {\map f \bsx - \map f \bsy} < \dfrac 1 {n + 1}$

Then $f$ is computably uniformly continuous.