Term for a correspondence of two point sets regarding their ordering in each dimension
Associate with $S$ and $S&#39;$ the posets $P = (\leq, S)$ and $P&#39; = (\leq, S&#39;)$, where $\leq$ is the dominance order in $\mathbb{R}^d$. The function you describe is an isomorphism between $P$ and $P&#39;$.