Nowhere dense sets corresponding to summable ideals
by
Jana Flašková
University of West Bohemia in Pilsen

If g: w→ [0, ∞) is a function such that lim_{n → ∞} g(n) = 0 and ∑_{n ∈ w} g(n) = ∞ then the family I_g = {A ⊆ w: ∑_{a ∈ A} g(a) < +∞} is a tall summable ideal on the set of all natural numbers. The set of all free ultrafilters on w which have empty intersection with a given summable ideal I_g is a nowhere dense subset of the remainder of Cech-Stone compactification of natural numbers. We investigate for which functions g the corresponding nowhere dense set is a solution to Problem 235. posed by K. P. Hart and J. van Mill in Open Problems in Topology: For what nowhere dense sets A ⊆ w^* do we have ∪_{p ∈ Sw} p[A] ≠ w^*?

Date received: June 24, 2008