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1992 | 141 | 3 | 257-268
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Topological spaces admitting a unique fractal structure

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Each homeomorphism from the n-dimensional Sierpiński gasket into itself is a similarity map with respect to the usual metrization. Moreover, the topology of this space determines a kind of Haar measure and a canonical metric. We study spaces with similar properties. It turns out that in many cases, "fractal structure" is not a metric but a topological phenomenon.
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  • Mathematics Department, Addis Ababa University D-O-2200 Greifswald, P.O. Box 1176, Addis Ababa, Ethiopia
  • Fachbereich Mathematik, Ernst-Moritz-Arndt-Universität, Germany
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