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arXiv · 1809.08595

Even unique intersection point can break OSC: an example

Kirill Kamalutdinov·Andrey Tetenov
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Abstract

This was a long-standing question since 90-ies whether one-point intersection property for a self-similar set implies open set condition. We answer this question negatively. We give an example of a totally disconnected self-similar set $K\subset \mathbb R$ which does not have open set condition and has minimal overlap of its pieces, that is, all intersections of its pieces $K_i\cap K_j,i\neq j$ are empty except only one, which is a single point.

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Kirill Kamalutdinov, Andrey Tetenov. 2018-09-23. Even unique intersection point can break OSC: an example. https://doi.org/10.1088/1361-6544/ab4e0e

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