17 citations · 33 across the 11 of their papers we have counts for
13 papers
Infinite random graphs
Ziemowit Kostana, Jarosław Swaczyna, Agnieszka Widz
We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, w…
Bourgain-uo sequential completeness in vector lattices
Tomasz Kania, Jarosław Swaczyna
We revisit Bourgain's 1981 counterexample to the sequential completeness of the `pointwise plus domination' convergence on from the perspective of vector lattices. In this…
The -property of a Banach space along a filter
Tomasz Kania, Jarosław Swaczyna
We examine the analyticity of the class of separable Banach spaces possessing the -property, defined in terms of convergence along a filter. Our results establish that this clas…
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…
How to get the random graph with non-uniform probabilities?
Leonardo N. Coregliano, Jarosław Swaczyna, Agnieszka Widz
The Rado Graph, sometimes also known as the (countable) Random Graph, can be generated almost surely by putting an edge between any pair of vertices with some fixed probability $p…
Free group of Hamel functions
Mateusz Lichman, Michał Pawlikowski, Szymon Smolarek +1
We construct a free group of continuum many generators among those autobijections of which are also Hamel bases of , with identity function included. We…
Continuity of coordinate functionals of filter bases in Banach spaces
Noé de Rancourt, Tomasz Kania, Jarosław Swaczyna
We prove that the coordinate functionals associated with filter bases in Banach spaces are continuous as long as the underlying filter is analytic. This removes the large-cardinal…
Large cardinals and continuity of coordinate functionals of filter bases in Banach spaces
Tomasz Kania, Jarosław Swaczyna
Assuming the existence of certain large cardinal numbers, we prove that for every projective filter over the set of natural numbers, -bases in Banach spac…
Connectedness of attractors of a certain family of IFSs
Filip Strobin, Jarosław Swaczyna
Let be a Banach space and be contractions. We investigate the set $$ C_{f,g}:=\{w\in X:\m{ the attractor of IFS }\F_w=\{f,g+w\}\m{ is connected}\}. $$ The…
Haar- sets: looking at small sets in Polish groups through compact glasses
Taras Banakh, Szymon Głąb, Eliza Jabłońska +1
Generalizing Christensen's notion of a Haar-null set and Darji's notion of a Haar-meager set, we introduce and study the notion of a Haar- set in a Polish group. Here $…
Properties of simple density ideals
Adam Kwela, Michał Popławski, Jarosław Swaczyna +1
Let consist of all functions with and . Then for each the family $\mathcal{Z}_g=\{A\subsete…
On generating regular Cantorvals connected with geometric Cantor sets
Artur Bartoszewicz, Małgorzata Filipczak, Szymon Głcab +2
We show that the Cantorvals connected with the geometric Cantor sets are not achievement sets of any series. However many of them are attractors of IFS consisting of affine functio…
A code space for a generalized IFS
Filip Strobin, Jarosław Swaczyna
We study the concept of a code (or shift) space for a generalized iterated function system (GIFS in short). We prove that relations between GIFSs and their code spaces are analogou…