Fine-Continuous Functions and Fractals Defined by Infinite Systems of Contractions
Motivated by our study in  of the graph of some Fine-computable (hence Fine-continuous) but not locally uniformly Fine-continuous functions defined according to Brattka’s idea in , 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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