\begin{definition}[Definition:Closure Operator (Matroid)]
Let $M = \struct{S, \mathscr I}$ be a matroid.
The '''closure operator''' of the matroid $M$ is the mapping $\sigma : \powerset S \to \powerset S$ defined by:
:$\map \sigma A$ is the set of elements of $S$ which depend on $A$
\end{definition}