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.
@article{bwmeta1.element.bwnjournal-article-fmv141i3p257bwm,
author = {Christoph Bandt and T. Retta},
title = {Topological spaces admitting a unique fractal structure},
journal = {Fundamenta Mathematicae},
volume = {141},
year = {1992},
pages = {257-268},
zbl = {0832.28011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv141i3p257bwm}
}
Bandt, Christoph; Retta, T. Topological spaces admitting a unique fractal structure. Fundamenta Mathematicae, Tome 141 (1992) pp. 257-268. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv141i3p257bwm/
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