Strong Duality Property for Matroids with Coefficients

The duality of infinite matroids with coefficients defined in [1] and the duality of Klee matroids [5], a generalization to the infinite case of matroid closure operators, are not identical. In this paper we characterize those Klee matroids arising as closure operators of matroids with coefficients. We study the subclass corresponding to the case in which both dualities coincide. These matroids with coefficients are said to have the strong duality property. Furthermore, in this case it is possible to define these matroids without matroid support systems.