Attractors for iterated function schemes on [0,1]N are exceptional

Let X = [0, 1](N) with S = {S-1,...,S-M} a finite set of contraction maps from X to itself. A nonempty compact subset E of X is an attractor for the iterated function scheme S if E = boolean OR(M)(i=1) S-i(E) = S(E). We show that the typical closed set in [0, 1](N) is not an attractor of any iterated function scheme. (C) 2014 Elsevier Inc. All rights reserved.