Real Analysis Exchange

A Non Self-Similar Set

Emma D’Aniello and T. H. Steele

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For each $s \in (0,1]$, we give an example of a nowhere dense perfect set $E$ contained in the unit interval with $\dim_{\cal H} (E) = s$, which is not an attractor for any iterated function system composed of weak contractions. This answers a problem posed by Zoltán Buczolich at the Summer Symposium in Real Analysis XXXIX (June 8-13, 2015, St.~Olaf College, Northfield, MN).

Article information

Real Anal. Exchange, Volume 41, Number 2 (2016), 347-350.

First available in Project Euclid: 30 March 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A18: Iteration [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25] 28A78: Hausdorff and packing measures
Secondary: 28A80: Fractals [See also 37Fxx]

iterated function system attractor self-similar set Cantor set


D’Aniello, Emma; Steele, T. H. A Non Self-Similar Set. Real Anal. Exchange 41 (2016), no. 2, 347--350.

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