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 …

IDEAL CONVERGENCE VERSUS MATRIX SUMMABILITY 1. Introduction The problem of
examining the relationship between ideal convergence Page 1 IDEAL CONVERGENCE …

We introduce a new ideal, related to the topology of Rizza defined on the set of positive
integers, and examine its basic properties. With the use of the Rizza's ideal we answer the …

We investigate ideals of the form {A⊆ ω: Σn∈ Axn is unconditionally convergent} where (xn)
n∈ ω is a sequence in a Polish group or in a Banach space. If an ideal on ω can be seen in …

For a free filter F on ω, let NF= ω∪{p F}, where p F∉ ω, be equipped with the following
topology: every element of ω is isolated whereas all open neighborhoods of p F are of the …

We consider the ideal of nowhere dense sets in the common division topology
(Szyszkowska's ideal), and examine some of its basic properties. We also explore the …

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

In recent works by L. Drewnowski and I. Labuda and J. Mart\'inez et al., non-pathological
analytic\(P\)-ideals and non-pathological\(F_\sigma\)-ideals have been characterized and …

The paper consists of two parts. In the first part (Section 3) we consider summability methods
for nonregular matrices (see Subsection 1.1 for an outline of the results). In the second part …

We continue our work on the ideal version of the Lévy–Steinitz theorem on conditionally
convergent series of vectors. In particular, we prove that for each series n ∈ ω v_n∑ n∈ ω …