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Topological spaces admitting a unique fractal structure. (English) Zbl 0832.28011
Summary: 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.

MSC:
28A80 Fractals
54E35 Metric spaces, metrizability
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