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Fine-Continuous Functions and Fractals Defined by Infinite Systems of Contractions

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Book cover Infinity in Logic and Computation (ILC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5489))

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Abstract

Motivated by our study in [12] of the graph of some Fine-computable (hence Fine-continuous) but not locally uniformly Fine-continuous functions defined according to Brattka’s idea in [2], we have developed a general theory of the fractal defined by an infinite system of contractions. In our theory, non-compact invariant sets are admitted. We note also that some of such fractals, including the graph of Brattka’s function, are also characterized as graph-directed sets. Furthermore, mutual identity of graph-directed sets and Markov-self-similar sets is established.

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References

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Author information

Authors and Affiliations

  1. Faculty of Science, Kyoto Sangyo University, 603-8555, Kyoto, Japan

    Yoshiki Tsujii, Takakazu Mori & Mariko Yasugi

  2. Graduate School of Human and Environmental Studies, Kyoto University, 606-8501, Kyoto, Japan

    Hideki Tsuiki

Authors
  1. Yoshiki Tsujii
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  2. Takakazu Mori
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  3. Mariko Yasugi
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  4. Hideki Tsuiki
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Cape Town, 7701, Rondebosch, South Africa

    Margaret Archibald  & Vasco Brattka  & 

  2. School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa

    Valentin Goranko

  3. Institute for Logic, Language and Computation, Universiteit van Amsterdam, 1090, Amsterdam, GE, The Netherlands

    Benedikt Löwe

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Tsujii, Y., Mori, T., Yasugi, M., Tsuiki, H. (2009). Fine-Continuous Functions and Fractals Defined by Infinite Systems of Contractions. In: Archibald, M., Brattka, V., Goranko, V., Löwe, B. (eds) Infinity in Logic and Computation. ILC 2007. Lecture Notes in Computer Science(), vol 5489. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03092-5_9

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  • DOI: https://doi.org/10.1007/978-3-642-03092-5_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03091-8

  • Online ISBN: 978-3-642-03092-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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