Accessible values of Assouad and the lower dimensions of subsets

Changhao Chen, Meng Wu, Wen Wu

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…