The number of field topologies on countable fields
The number of field topologies on countable fields
J. O. Kiltinen proves that every infinite field admits a nondiscrete, Hausdorff field topology. In this note it is shown that every countable field $K$ admits ${2^{{2^{{\aleph _0}}}}}$ many field topologies, which even fail to be the join of locally bounded ring topologies.