Abstract

This was a long-standing question since 90s whether one-point intersection property for a self-similar set implies open set condition (OSC). We answer this question negatively. We give an example of a totally disconnected self-similar set K ⊂ ℝ which does not have OSC and has minimal overlap of its pieces, that is, all intersections of its pieces Ki∩Kj, i≠j are empty except only one, which is a single point.

Original languageEnglish
Pages (from-to)408-416
Number of pages9
JournalNonlinearity
Volume33
Issue number1
DOIs
Publication statusPublished - 1 Jan 2020

Keywords

  • general position theorem
  • Hausdorff dimension
  • open set condition
  • self-similar set
  • weak separation property

Fingerprint Dive into the research topics of 'On one-point intersection property for self-similar fractals'. Together they form a unique fingerprint.

  • Cite this