Matroids

Matroids are an abstraction of Vector Spaces.  Vectors spaces have addition and scalar multiplication and the axioms of vectors spaces lead to the concepts of subspaces, rank, and independent sets.  All Vector Spaces are Matroids, but Matroids only retain the properties of independence, rank, and subspaces. The idea of the Matroid closure of a set is the same as the span of the set in the Vector Space.