Let $M_X = (X, d_X)$ and $M_Y = (Y, d_Y)$ each be a D1107: Metric space.
A D18: Map $f : X \to Y$ is a Hölder map from $M_X$ to $M_Y$ if and only if \begin{equation} \exists \, C, \alpha > 0 : \forall \, x, y \in X : d_Y( f(x), f(y) ) \leq C d_X(x, y)^{\alpha} \end{equation}