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.
Предметные области OECD FOS+WOS
- 1.01.PN МАТЕМАТИКА, ПРИКЛАДНАЯ
- 1.01.UR ФИЗИКА, МАТЕМАТИЧЕСКАЯ