# David Fernández Bretón: d=c implies that there are gruff ultrafilters

Thursday, February 25, 4:00-5:30 PM at CC Little 2502 (note the nonstandard building/room!!!)

I will show a proof of the statement in the title. Recall that a gruff ultrafilter was defined by van Douwen to be an ultrafilter on the rational numbers with a base of perfect subsets (where perfect means both closed (in the topology inherited from the usual Euclidean one from the reals) and crowded (without isolated points)). The main question, which to date is still open, regarding these objects is whether one can prove their existence in ZFC.