An ideal on a set X is a collection of subsets of X closed under the operations of taking finite
unions and subsets of its elements. Ideals are a very useful notion in topology and set theory …

We study the interplay between Banach space theory and theory of analytic P-ideals.
Applying the observation that, up to isomorphism, all Banach spaces with unconditional …

Let-convergent (and bounded). This allows us to establish the relationship between the
classical Silverman–Toeplitz characterization of regular matrices and its multidimensional …

This paper studies the combinatorics of ideals which recently appeared in ergodicity results
for analytic equivalence relations. The ideals have the following topological representation …

Let x be a sequence taking values in a separable metric space and let I be an F σ δ-ideal on
the positive integers (in particular, I can be any Erdős–Ulam ideal or any summable ideal). It …

The paper considers several different kinds of ideals defined by some densities. We depict
relationships between Erdős-Ulam, density, matrix summability and generalized density …

We provide necessary and/or sufficient conditions on vector spaces V of real sequences to
be a Fréchet space such that each coordinate map is continuous, that is, to be a locally …

We study ultrafilters on countable sets and reaping families which are indestructible by
Sacks forcing. We deal with the combinatorial characterization of such families and we prove …

For a family F⊆ ω ω we define the ideal I (F) on ω× ω to be the ideal generated by the family
{A⊆ ω× ω:∃ f∈ F∀∞ n (|{k:(n, k)∈ A}|≤ f (n))}. Using ideals of the form I (F), we show that …

Given a dynamical system $(X, T) $ and a family $\mathsf {I}\subseteq\mathcal {P}(\omega) $
of" small" sets of nonnegative integers, a point $ x\in X $ is said to be $\mathsf {I} $-strong …