Self-similar sets 4. Topology and measures. (English) Zbl 0779.54022

Bandt, Christoph

Topology and measure V, Proc. 5th Conf., Binz/Germany 1987, Wiss. Beitr. Ernst-Moritz-Arndt-Univ. Greifswald, 8-16 (1988).

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[For the entire collection see Zbl 0701.00012.]
For Part 3 see [Monatsh. Math. 108, No. 2/3, 89-102 (1989; Zbl 0712.58039)].
Self-similar sets were defined rigorously by J. E. Hutchinson [Indiana Univ. Math. J. 30, 713-747 (1981; Zbl 0598.28011)]. They are compact metric spaces – so far all examples were taken in \(E^ n\) – connected with a number of interesting questions concerning topology as well as measure theory. …Self-similar sets evidently have metric properties. We went to demonstrate that they also constitute an interesting class of topological spaces. …

MSC:

54E40	Special maps on metric spaces
28A80	Fractals
37B99	Topological dynamics
54H20	Topological dynamics (MSC2010)

Keywords:

contractions; fractal; Self-similar sets

Citations:

Zbl 0743.58027; Zbl 0707.28004; Zbl 0701.00012; Zbl 0712.58039; Zbl 0598.28011