Abstract
In this paper, we construct a self-similar set which has a best covering but it is not the natural covering, thus negate the conjecture on self-similar sets posed by Z. Zhou in 2004.
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Supported in part by the Foundations of the National Natural Science Committee(No.10572154), Jiangxi Province Natural Science Committee(No.0611005) and the Foundation of Education Ministry, Jiangxi Province (No.[2006]239), China.
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Jia, B., Xu, S. An answer to a conjecture on self-similar sets. Analys in Theo Applic 23, 9–15 (2007). https://doi.org/10.1007/s10496-001-0009-0
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DOI: https://doi.org/10.1007/s10496-001-0009-0