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MiS Preprint

A notion of Euler characteristic for fractals

Marta Llorente and Steffen Winter


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.

MSC Codes:
28A80, 52A38, 26B15
euler characteristic, self-similar sets, renewal theorem

Related publications

2007 Repository Open Access
Marta Llorente and Steffen Winter

A notion of Euler characteristic for fractals

In: Mathematische Nachrichten, 280 (2007) 1/2, pp. 152-170