Attractors of iterated function systems with uncountably many maps and infinite sums of Cantor sets
The authors consider iterated function systems on the real line, consisting of affine maps of homogeneous contraction ratio, and study the topological properties of their attractors. There are uncountably many such objects and the set of their fixed points is a Cantor set. They prove that, under specific hypotheses, such attractors consist of the union of a finite number of closed intervals, and a more general result for infinite sums of compact sets, in the sense of Minkowski and under the Hausdorff metric.
scientific article; zbMATH DE number 6808298