If for any finite subset M of a countable skew field R there exists an infinite subset S  R such that r · m = m · r for any r 2 S and for any m 2 M, then the skew field R admits: – A non-discrete Hausdorff skew field topology 0. – Continuum of non-discrete Hausdorff skew field topologies which are stronger than the topology 0 and such that sup{1, 2} is the discrete topology for any different topologies 1 and 2; – Continuum of non-discrete Hausdorff skew field topologies which are stronger than 0 and such that any two of these topologies are comparable; – Two to the power of continuum Hausdorff skew field topologies stronger than 0, and each of them is a coatom in the lattice of all skew field topologies of the skew fields.