Description

• Title:
  Topological and measure properties of some self-similar sets
• Creator:
  Banakh, Taras;
  Bartoszewicz, Artur;
  Szymonik, Emilia;
  Filipczak, Małgorzata
• Description:
  Given a finite subset $\Sigma \subset \mathbbR$ and a positive real number $q<1$ we study topological and measure-theoretic properties of theself-similar set $K(\Sigma ;q)=\bigg\\sum\limits_n=0^\inftya_nq^n:(a_n)_n\in \omega \in \Sigma ^\omega \bigg\$, which is theunique compact solution of the equation $K=\Sigma +qK$. The obtained resultsare applied to studying partial sumsets $E(x)=\bigg\\sum\limits_n=0^\inftyx_n\varepsilon _n:(\varepsilon _n)_n\in \omega \in \0,1\^\omega %\bigg\$ of multigeometric sequences $x=(x_n)_n\in \omega $. Such setswere investigated by Ferens, Mor\'an, Jones and others. The aim of thepaper is to unify and deepen existing piecemeal results.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 46, No 2 (December 2015); 1013 - 1028;
  1230-3429
• Format:
  application/pdf
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.075/7272 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2015.075/7309
• Subject:
  Self-similar set;
  multigeometric sequence;
  Cantorval;
  40A05;
  28A80;
  11K31
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.075
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other