Size of the set of attractors for iterated function systems

We discuss the smallness of the set of attractors for iterated function systems. This paper is an attempt to measure the difference between the family of IFS attractors and a broader family, the set of attractors for the weak iterated function systems. We prove that the IFS attractors form a σ-porous subset of K([0, 1]d), the family of compact subsets of a metric space [0, 1]d. We also show that weak IFS attractors form a first category set.