## Real Analysis Exchange

### A Non Self-Similar Set

#### 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).

#### Article information

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

Dates
First available in Project Euclid: 30 March 2017