On closure axioms for a matroid using Galois connections

We present two systems of closure axioms for a matroid with the assistance of Galois connections. These axioms give a mathematical foundation for the connections between matroids, Galois connections and concept lattices. We deal with some relationship between matroids and geometric lattices by the above axioms. We also discuss some applications between matroids and concept lattices with the above two closure axioms for a matroid