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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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
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