\begin{definition}[Definition:Set Meeting Set]
Let $\family {S_i}_{i \mathop \in I}$ be an family of sets indexed by some  indexing set $I$.
The sets in $\family {S_i}$ are said to '''meet''' {{iff}} their intersection is not empty.
That is, {{iff}}:
:$\ds \bigcap_{i \mathop \in I} \family {S_i} \ne \O$
That is, {{iff}} $\family {S_i}_{i \mathop \in I}$ is not disjoint.
\end{definition}