Attila Joó, Base partition for finitary-cofinitary matroid families

Let $\mathcal{M}=(M_i:i\in K)$ be a finite or infinite family consisting of finitary and cofinitary matroids on a common ground set $E$.

We prove the following Cantor-Bernstein-type result: if $E$ can be covered by sets $(B_i:i\in K)$ which are bases in the corresponding matroids and there are also pairwise disjoint bases of the matroids $M_i$ then $E$ can be partitioned into bases with respect to $\mathcal{M}$.