There may be no nowhere dense ultrafilter
Abstract
We show the consistency of ZFC +''there is no NWD-ultrafilter on omega'', which means: for every non principle ultrafilter D on the set of natural numbers, there is a function f from the set of natural numbers to the reals, such that for some nowhere dense set A of reals, the set n: f(n) in A is not in D. This answers a question of van Douwen, which was put in more general context by Baumgartner
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