Description

• Title:
  Characterization of the algebraic difference of special affine Cantor sets
• Creator:
  Nowakowski, Piotr
• Description:
  We investigate some self-similar Cantor sets $C(l,r,p)$, which we call S-Cantor sets, generated by numbers $l,r,p \in \N$, $l+r< p$. We give a full characterization of the set $C(l_1,r_1,p)-C(l_2,r_2,p)$ which can take one of the form: the interval $[-1,1]$, a Cantor set, an L-Cantorval, an R-Cantorval or an M-Cantorval. As corollaries we give examples of Cantor sets and Cantorvals, which can be easily described using some positional numeral systems.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2024 Piotr Nowakowski
• Date:
  2024.09.15
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 64, No 1 (September 2024); 295 - 316;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/55212/39693 ;https://apcz.umk.pl/TMNA/article/view/55212/39694
• Subject:
  Cantor sets;
  Cantorvals;
  algebraic difference of sets;
  p-adic sets;
  sets of P-sums;
  28A80, 05B10, 11A67
• Identifier: https://apcz.umk.pl/TMNA/article/view/55212
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other