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Self-similar sets with an open set condition and great variety of overlaps |
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| Authors: | Christoph Bandt Nguyen Viet Hung |
| Affiliation: | Institute for Mathematics and Informatics, Arndt University, 17487 Greifswald, Germany ; Department of Mathematics, Hue University, Hue, Vietnam |
| Abstract: | For a very simple family of self-similar sets with two pieces, we prove, using a technique of Solomyak, that the intersection of the pieces can be a Cantor set with any dimension in ![$ [0,0.2]$](http://www.ams.org/proc/2008-136-11/S0002-9939-08-09349-0/gif-abstract0/img1.gif){kind=small} as well as a finite set of any cardinality  . The main point is that the open set condition is fulfilled for all these examples. |
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