Definition 1.14 ( $d$ -dimensional space). A $d$ -dimensional space $S \subseteq X^{n}$ or a $d$ -point parameter set is a set such that there exists $I_{1}, I_{2}, \dots, I_{d} \subseteq [n]$ disjoint and $a_{i} \in X \forall i \in [n] ∖ (I_{1} \cup \dots \cup I_{d})$ , and $x \in S$ if and only if:

$x_{i} = a_{i}$ for all $i \in [n] ∖ (I_{1} \cup \dots \cup I_{d})$
$x_{i} = x_{i}$ if $i, j \in I_{d}$ for some $l \in [d]$