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On the structure of self-similar sets

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Abstract

We shall investigate topological properties of a uniquely determined compact setK such thatK = Σ λ ∈Λ f λ (K), where eachf λ is a weak contraction of a complete metric space andΛ = {1,2,...,m} orΛ =N. Such a setK is said to be self-similar. Many classical peculiar sets can be represented in this form. We shall also discuss the interesting problem presented by R. F. Williams.

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  1. Department of Mathematics, Faculty of Science, Kyoto University, 606, Kyoto, Japan

    Masayoshi Hata

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  1. Masayoshi Hata
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Hata, M. On the structure of self-similar sets. Japan J. Appl. Math. 2, 381–414 (1985). https://doi.org/10.1007/BF03167083

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  • DOI: https://doi.org/10.1007/BF03167083

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