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Accessible values of Assouad and the lower dimensions of subsets
Published 5 Feb 2016 in math.MG | (1602.02180v1)
Abstract: Let $E$ be a subset of a doubling metric space $(X,d)$. We prove that for any $s\in [0, \dim_{A}E]$, where $\dim_{A}$ denotes the Assouad dimension, there exists a subset $F$ of $E$ such that $\dim_{A}F=s$. We also show that the same statement holds for the lower dimension $\dim_L$.
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