Hausdorff ultrafilters

We give the name Hausdorff to those ultrafilters that provide ultrapowers whose natural topology (S-topology) is Hausdorff, e.g. selective ultra. lters are Hausdorff. Here we give necessary and sufficient conditions for product ultra. lters to be Hausdorff. Moreover we show that no regular ultrafilter over the "small" uncountable cardinal u can be Hausdorff. (u is the least size of an ultrafilter basis on w.) We focus on countably incomplete ultra. lters, but our main results also hold for kappa-complete ultrafilters.