A. Kwela

activity

20132026

most citedHomogeneous ideals on countable sets

22 citations · 105 across the 33 of their papers we have counts for

collaborators

39 papers

math.FA2026

Characterized subgroups on the unit circle

Rafal Filipow, Adam kwela, Paolo Leonetti +1

Given an ideal $I$ on $ω$ , a subgroup $H$ of the unit circle $T$ is said to be $I$ -characterized if there exists an integer sequence $a = (a_{n} : n \in ω)$ …

math.GN2026

Are scales Fréchet?

Raul Figueroa-Sierra, Osvaldo Guzmán, Michael Hrušák +1

We continue the study of Dow spaces of a $b$ -scale, originally introduced by Alan Dow in " $π$ -Weight and the Fréchet-Urysohn property" (Topology and its Applications, Vo…

math.GN2026

A new order for ideal sequential compactness

Adam Kwela, Dorota Lesner

Let $I$ be an ideal on $ω$ and $X$ be a topological space. A sequence $(x_{n})_{n \in ω}$ in $X$ is $I$ -convergent if there is $x \in X$ such that $\{n\in ω:x_n\not…

math.GN2026

Sets of Ramsey-limit points and IP-limit points

Rafał Filipów, Adam Kwela, Paolo Leonetti

Let $X$ be an uncountable Polish space and let $H$ be the Hindman ideal, that is, the family of all $S \subseteq ω$ which are not $I P$ -sets. For each sequence $x=(x_n)_{n…

math.GN2026

Critical partition regular functions for compact spaces

Rafał Filipów, Małgorzata Kowalczuk, Hubert Książek +2

We study ideal-based refinements of sequential compactness arising from the class FinBW(I), consisting of topological spaces in which every sequence admits a convergent subsequence…

math.FA2025

Zoo of ideal Schauder basis

Adam Kwela, Jarosław Swaczyna

We investigate the notion of filter (equivalently: ideal) Schauder basis of a Banach space. We do so by providing bunch of new examples of such bases that are not the standard ones…

math.LO2025

Two $b$ or not two $b$ ?

Rafał Filipów, Adam Kwela

The paper is devoted to comparison of two generalizations of the bounding number $b$ .

math.GN2025

Critical ideals for compact spaces

Rafał Filipów, Małgorzata Kowalczuk, Adam Kwela

For each countable ordinal $α$ , we introduce an ideal $co n v_{α}$ and use it to characterize the class of all compact countable spaces which are homeomorphic to the space $ω^α\cdot n+…

math.FA2025

Compactness in spaces of functions of bounded variation from ideal perspective

Jacek Gulgowski, Adam Kwela, Jacek Tryba

Recently we have presented a unified approach to two classes of Banach spaces defined by means of variations (Waterman spaces and Chanturia classes), utilizing the concepts from th…

math.GN2024

Borel complexity of sets of ideal limit points

Rafal Filipow, Adam Kwela, Paolo Leonetti

Let $X$ be an uncountable Polish space and let $I$ be an ideal on $ω$ . A point $η \in X$ is an $I$ -limit point of a sequence $(x_{n})$ taking values in $X$ if ther…

math.FA2024

Functions of bounded variation from ideal perspective

Jacek Gulgowski, Adam Kwela, Jacek Tryba

We present a unified approach to two classes of Banach spaces defined with the aid of variations: Waterman spaces and Chanturia classes. Our method is based on some ideas coming fr…

math.LO2024

More on yet another ideal version of the bounding number

Adam Kwela

This is a continuation of the paper [J. Symb. Log. 87 (2022), 1065--1092]. For an ideal $I$ on $ω$ we denote $\mathcal{D}_{\mathcal{I}}=\{f\inω^ω: f^{-1}[\{n\}]\in\mathca…

math.LO2023

Egorov ideals

Adam Kwela

We study Egorov ideals, that is ideals on $ω$ for which the Egorov's theorem for ideal versions of pointwise and uniform convergences holds. We show that a non-pathological $\bf{Σ^…

math.GN2023★ 5 cited

New Hindman spaces

Rafał Filipów, Krzysztof Kowitz, Adam Kwela +1

We introduce a method that allows to turn topological questions about Hindman spaces into purely combinatorial questions about the Katětov order of ideals on $N$ . We also…

math.LO2023★ 6 cited

Characterizing existence of certain ultrafilters

Rafał Filipów, Krzysztof Kowitz, Adam Kwela

Following Baumgartner [J. Symb. Log. 60 (1995), no. 2], for an ideal $I$ on $ω$ , we say that an ultrafilter $U$ on $ω$ is an $I$ -ultrafilter if for ev…

math.GN2023

Spaces not distinguishing ideal pointwise and $σ$ -uniform convergence

Rafał Filipów, Adam Kwela

We examine topological spaces not distinguishing ideal pointwise and ideal $σ$ -uniform convergence of sequences of real-valued continuous functions defined on them. For instance, w…

math.LO2023★ 4 cited

Yet another ideal version of the bounding number

Rafał Filipów, Adam Kwela

Let $I$ be an ideal on $ω$ . For $f, g \in ω^{ω}$ we write $f \leq_{I} g$ if $f (n) \leq g (n)$ for all $n \in ω ∖ A$ with some $A \in I$ . Moreover, we den…

math.GN2023

A unified approach to Hindman, Ramsey and van der Waerden spaces

Rafał Filipów, Krzysztof Kowitz, Adam Kwela

For many years, there have been conducting research (e.g. by Bergelson, Furstenberg, Kojman, Kubiś, Shelah, Szeptycki, Weiss) into sequentially compact spaces that are, in a sense,…

math.LO2023★ 1 cited

Katětov order between Hindman, Ramsey, van der Waerden and summable ideals

Rafał Filipów, Krzysztof Kowitz, Adam Kwela

A family I of subsets of a set X is an ideal on X if it is closed under taking subsets and finite unions of its elements. An ideal I on X is below an ideal J on Y in the Katetov or…

math.CA2023★ 1 cited

The ideal test for the divergence of a series

Rafał Filipów, Adam Kwela, Jacek Tryba

We generalize the classical Olivier's theorem which says that for any convergent series $\sum_{n} a_{n}$ with positive nonincreasing real terms the sequence $(n a_{n})$ tends to zero. Ou…

math.DS2021

Porosities of the sets of attractors

Paweł Klinga, Adam Kwela

This paper is another attempt to measure the difference between the family $A [0, 1]$ of attractors for iterated function systems acting on $[0, 1]$ and a broader family, the set $A_w…

math.DS2021★ 1 cited

Comparison of the sets of attractors for systems of contractions and weak contractions

Paweł Klinga, Adam Kwela

For $n, d \in N$ we consider the families: - $L_{n}^{d}$ of attractors for iterated function systems (IFS) consisting of $n$ contractions acting on $[0, 1]^{d}$ , - $w L_{n}^{d}$ of attra…

math.DS2021

Borel complexity of the family of attractors for weak IFSs

Paweł Klinga, Adam Kwela

This paper is an attempt to measure the difference between the family of iterated function systems attractors and a broader family, the set of attractors for weak iterated function…

math.LO2021

On a conjecture of Debs and Saint Raymond

Adam Kwela

Borel separation rank of an analytic ideal $I$ on $ω$ is the minimal ordinal $α < ω_{1}$ such that there is $S \in Σ_{1 + α}^{0}$ with $\mathcal{I}\subseteq \mathc…

Characterized subgroups on the unit circle

Are scales Fréchet?

A new order for ideal sequential compactness

Sets of Ramsey-limit points and IP-limit points

Critical partition regular functions for compact spaces

Zoo of ideal Schauder basis

Two b or not two b?

Critical ideals for compact spaces

Compactness in spaces of functions of bounded variation from ideal perspective

Borel complexity of sets of ideal limit points

Functions of bounded variation from ideal perspective

More on yet another ideal version of the bounding number

Egorov ideals

New Hindman spaces

Characterizing existence of certain ultrafilters

Spaces not distinguishing ideal pointwise and σ-uniform convergence

Yet another ideal version of the bounding number

A unified approach to Hindman, Ramsey and van der Waerden spaces

Katětov order between Hindman, Ramsey, van der Waerden and summable ideals

The ideal test for the divergence of a series

Porosities of the sets of attractors

Comparison of the sets of attractors for systems of contractions and weak contractions

Borel complexity of the family of attractors for weak IFSs

On a conjecture of Debs and Saint Raymond

Two $b$ or not two $b$ ?

Spaces not distinguishing ideal pointwise and $σ$ -uniform convergence