Topological spaces admitting a unique fractal structure
Volume 141 / 1992
Fundamenta Mathematicae 141 (1992), 257-268
DOI: 10.4064/fm-141-3-257-268
Abstract
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.
