is not subsequential
If a separable dense in itself metric space is not a union of countably many nowhere dense subsets, then its -space is not subsequential.
If a separable dense in itself metric space is not a union of countably many nowhere dense subsets, then its -space is not subsequential.
Fréchet, strongly Fréchet, productively Fréchet, weakly bisequential and bisequential filters (i.e., neighborhood filters in spaces of the same name) are characterized in a unified manner in terms of their images in the Stone space of ultrafilters. These characterizations involve closure structures on the set of ultrafilters. The case of productively Fréchet filters answers a question of S. Dolecki and turns out to be the only one involving a non topological closure structure.