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 language | English |
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Pages (from-to) | 408-416 |
Number of pages | 9 |
Journal | Nonlinearity |
Volume | 33 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2020 |
Keywords
- general position theorem
- Hausdorff dimension
- open set condition
- self-similar set
- weak separation property
OECD FOS+WOS
- 1.01.PN MATHEMATICS, APPLIED
- 1.01.UR PHYSICS, MATHEMATICAL