Continuous dependence of attractors of iterated function systems
The author observes that in the book [\textit{M. Barnsley}, Fractals everywhere (1988; Zbl 0691.58001)] the proof of a true theorem concerning the continuous dependence of the attractors on the parameter is based on a false lemma. He extends the result in question showing among others that the assumption of compactness of the parameter space is superfluous. Moreover he proves that a Banach space is finite-dimensional if, and only if, whenever a sequence of its contraction selfmaps converges pointwise to a contraction mapping \(A\), then the sequence of their fixed points converges to the fixed point of \(A\).
scientific article; zbMATH DE number 902496