Let $V_1$ and $V_2$ be two metric vector spaces over $\mathbb{R}$. Let $f: V_1 \rightarrow V_2$ with the following property:
$\forall \vec{x},\vec{y},\vec{z} \in V_1$ such that $\vec{x} \cdot \vec{y} \lt \vec{x} \cdot \vec{z}$, then $f(\vec{x}) \cdot f(\vec{y}) \lt f(\vec{x}) \cdot f(\vec{z})$
Is there a name for such a function property? Or for a related property (eg. relating angles between input/output vectors and not complete scalar product)?
(Context: dimensionality reduction)