A Remark on Special Class of Functions

A line closure function $mathcal{L (S) }$ is defined as union of all lines connecting $2$ distinct points $A$ and $B$ in $mathbb{S}$. $mathcal{L (S) }$ order n is a function $mathcal{L (S) }$ applied to a set $S$, n times. We explore the minimum amount of times we need to take a line closure of a set of $n + 1$points in n space until the entire $n$-plane is covered.