Abstract
Consider a metric space (X,d) that is separable, 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˜). The main goal of this study is to explore a relationship between the general fractal dimensions of the set Z⊂X and their counterparts in the space of compact subsets K(Z)⊂K(X).
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