Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Swaczyna, Jarosław"'
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 $p \in (0, 1)$, independently of other pairs. In this article, we study t
Externí odkaz:
http://arxiv.org/abs/2405.16142
We construct a free group of continuum many generators among those autobijections of $\mathbb{R}$ which are also Hamel bases of $\mathbb{R}^2$, with identity function included. We also observe two new cases when a real function is a composition of tw
Externí odkaz:
http://arxiv.org/abs/2306.12445
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 hypothesis from the result established by the two last-named authors (
Externí odkaz:
http://arxiv.org/abs/2203.15123
Autor:
Kania, Tomasz, Swaczyna, Jarosław
Assuming the existence of certain large cardinal numbers, we prove that for every projective filter $\mathscr F$ over the set of natural numbers, $\mathscr{F}$-bases in Banach spaces have continuous coordinate functionals. In particular, this applies
Externí odkaz:
http://arxiv.org/abs/2005.04873
Publikováno v:
In Journal of Functional Analysis 1 May 2023 284(9)
Autor:
Strobin, Filip, Swaczyna, Jarosław
Let $X$ be a Banach space and $f,g:X\rightarrow X$ 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 motivation for our research comes from papers of Mihail and Miculescu,
Externí odkaz:
http://arxiv.org/abs/1812.06427
Publikováno v:
Dissert.Math. 564 (2021), 1-105
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-$\mathcal I$ set in a Polish group. Here $\mathcal I$ is an ideal of subsets of some compact metrizable space $K
Externí odkaz:
http://arxiv.org/abs/1803.06712
Let $G$ consist of all functions $g \colon \omega \to [0,\infty)$ with $g(n) \to \infty$ and $\frac{n}{g(n)} \nrightarrow 0$. Then for each $g\in G$ the family $\mathcal{Z}_g=\{A\subseteq\omega:\ \lim_{n\to\infty}\frac{\text{card}(A\cap n)}{g(n)}=0\}
Externí odkaz:
http://arxiv.org/abs/1711.02663
Autor:
Bartoszewicz, Artur, Filipczak, Małgorzata, Głcab, Szymon, Prus-Wiśniowski, Franciszek, Swaczyna, Jarosław
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 functions.
Externí odkaz:
http://arxiv.org/abs/1706.03523
Autor:
Strobin, Filip, Swaczyna, Jarosław
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 analogous to the case of classical IFSs. As an application, we consider the pr
Externí odkaz:
http://arxiv.org/abs/1310.3097