Topological spaces admitting a unique fractal structure

Christoph Bandt; T. Retta

Fundamenta Mathematicae (1992)

  • Volume: 141, Issue: 3, page 257-268
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Bandt, Christoph, and Retta, T.. "Topological spaces admitting a unique fractal structure." Fundamenta Mathematicae 141.3 (1992): 257-268. <http://eudml.org/doc/211964>.

@article{Bandt1992,
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.},
author = {Bandt, Christoph, Retta, T.},
journal = {Fundamenta Mathematicae},
keywords = {edge-balanced graphs; critical points; topological spaces; fractal structure; Sierpiński gasket; similarity map; Haar measure},
language = {eng},
number = {3},
pages = {257-268},
title = {Topological spaces admitting a unique fractal structure},
url = {http://eudml.org/doc/211964},
volume = {141},
year = {1992},
}

TY - JOUR
AU - Bandt, Christoph
AU - Retta, T.
TI - Topological spaces admitting a unique fractal structure
JO - Fundamenta Mathematicae
PY - 1992
VL - 141
IS - 3
SP - 257
EP - 268
AB - 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.
LA - eng
KW - edge-balanced graphs; critical points; topological spaces; fractal structure; Sierpiński gasket; similarity map; Haar measure
UR - http://eudml.org/doc/211964
ER -

References

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