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MiS Preprint
31/2004

A notion of Euler characteristic for fractals

Marta Llorente and Steffen Winter

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.

Received:
14.05.2004
Published:
14.05.2004
MSC Codes:
28A80, 52A38, 26B15
Keywords:
euler characteristic, self-similar sets, renewal theorem

Related publications

inJournal
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