In a recent paper, Bruhn, Diestel, Kriesell and Wollan (arXiv:1003.3919)
present four systems of axioms for infinite matroids, in terms of independent
sets, bases, closure and circuits. No system of rank axioms is given. We give
an easy example showing that rank function of an infinite matroid may not
suffice to characterize it. We present a system of axioms in terms of relative
rank.Comment: The results in this paper have now been merged into arXiv:1003.391