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

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5489)


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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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Faculty of ScienceKyoto Sangyo UniversityKyotoJapan
  2. 2.Graduate School of Human and Environmental StudiesKyoto UniversityKyotoJapan

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