Posets and Closure Operators Relative to Matroids

Using the closure operator axioms for a matroid presented here, for all the matroids defined on the same ground set E, two posets are provided: one is consisted by the system of the closure operators of all these matroids; another is instructed by the system of all these matorids. Additionally, when the set E is finite, by graph theory, two different skecthes to search out all the matroids defined on E are given.