Abstract:The topological and metrical equivalence of fractals is an important topic in analysis. In this paper, we use a class of finite state automata, called Σ-automaton, to construct psuedo-metric spaces, and then apply them to the study of classification of self-similar sets. We first introduce a notion of topology automaton of a fractal gasket, which is a simplified version of neighbor automaton; we show that a fractal gasket is homeomorphic to the psuedo-metric space induced by the topology automaton. Then we con… Show more
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