A Cantor-Bernstein theorem for infinite matroids

Abstract

Let M 0 and M 1 be matroids on E having only finitary and cofinitary components and let X i ⊆ E for i ∈ {0, 1}. We show that if X i can be spanned in M i by an M 1−i -independent set for i ∈ {0, 1}, then there is a common independent set I with X i ⊆ span Mi (I) for i ∈ {0, 1}. As an application we derive an analogue of Pym's theorem in compact graph-like spaces. We also prove a packing-covering-partitioning type of result for matroid families that generalizes the base partitioning theorem [1] of Erde et al.