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Let $(X,d)$ be a compact metric space. Assume that $f:X\to \mathbb{R}$ is a positive continuous function. We say that the $f$-dimension of $(X,d)$ is equal to $0$ if for every $\epsilon>0$ ...

Let $(X,d)$ be a compact metric space and recall that the $\epsilon$-external covering number $\mathcal{N}^{\epsilon}(X)$ of $X$ is defined by: $$ \mathcal{N}^{\epsilon}(X) := \inf\left\{ N\in \mathbb{...