arXiv subjects

Malgorzata Filipczak

Publications and source records attributed to Malgorzata Filipczak.

3 recordsLinked to original sources

arXiv2014

Topological and measure properties of some self-similar sets

Given a finite subset $Σ\subset\mathbb{R}$ and a positive real number $q<1$ we study topological and measure-theoretic properties of the self-similar set $K(Σ;q)=\big\{\sum_{n=0}^\infty a_nq^n:(a_n)_{n\inω}\inΣ^ω\big\}$, which is the unique compact solution of the equation $K=Σ+qK$. The obtained results are applied to studying partial sumsets $E(x)=\big\{\sum_{n=0}^\infty x_n\varepsilon_n:(\varepsilon_n)_{n\inω}\in\{0,1\}^ω\big\}$ of some (multigeometric) sequences $x=(x_n)_{n\inω}$.

math.GN↗

arXiv2013

Strong c-algebrability of strong Sierpiński-Zygmund, smooth nowhere analytic and other sets of functions

We present a useful technique of proving strong $\mathfrak{c}$-algebrability. As an outcome we obtain the strong $\mathfrak{c}$-algebrability of the following sets of functions: strong Sierpiński-Zygmund, nowhere Hölder, Bruckner-Garg, nowhere monotone differentiable, a certain Baire class, smooth and nowhere analytic functions.

math.RA↗

arXiv2013

Nonseparable spaceability and strong algebrability of sets of continuous singular functions

Let CBV denote the Banach algebra of all continuous real-valued functions of bounded variation, defined in [0,1]. We show that the set of strongly singular functions in CBV is nonseparably spaceable. We also prove that certain families of singular functions constitute strongly c-algebrable sets. The argument is based on a new general criterion of strong c-algebrability.

math.FA↗