Abstract
Consider a separable metric space (X,d), and let (K(X),d˜) denote the space of non-empty compact subsets of X equipped with the Hausdorff metric. This paper aims to introduce and investigate the concepts of two general fractal dimensions and general dimensions within the framework of (K(X),d˜). In particular, we explore a relationship between the general fractal dimensions of a set Z of a self-similar sequence space and their counterparts in the space of compact subsets K(Z).
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