Defining a mathematical strucutre with a collection of subsets gives rise to many known structures. We consider an abstract set X and the power set on whom. Then we pick the subsets we like. We therefor call such a collection of subsets a collection.

(X,C) \qquad X \ \ \ abstract \ set \qquad  C \ \ \ Collection

More formally the power set is defined as the set of all subsets of X.

\mathcal{\textcolor{gray}{P}}(X) := \Big\{ S \subseteq X \Big\}

and a collection is a nonempty subset of the power set.

C \subseteq \mathcal{\textcolor{gray}{P}}(X)\qquad C \neq \emptyset