# Topological spaces admitting a unique fractal structure

Fundamenta Mathematicae (1992)

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

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topBandt, 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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