A notion of Euler characteristic for fractals

Marta Llorente and Steffen Winter

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Submission date: 14. May. 2004
Pages: 31
published in: Mathematische Nachrichten, 280 (2007) 1/2, p. 152-170 
DOI number (of the published article): 10.1002/mana.200410471
Bibtex
MSC-Numbers: 28A80, 52A38, 26B15
Keywords and phrases: euler characteristic, self-similar sets, renewal theorem
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Abstract:
A notion of (average) fractal Euler number for subsets in the Euclidean space with infinite singular complexes is introduced by means of rescaled Euler numbers of infinitesimal r-neighbourhoods. For certain classes of self-similar sets we calculate the associated Euler exponent and the (average) fractal Euler number with the help of the renewal theorem. Examples like the Sierpinski gasket or carpet are provided.