Abstract
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).
Citation
Emma D’Aniello. T. H. Steele. "A Non Self-Similar Set." Real Anal. Exchange 41 (2) 347 - 350, 2016.
