Ahlfors regular spaces have regular subspaces of any dimension

Abstract

We characterize $Q$-dimensional Ahlfors regular spaces among trees' boundaries and show how to construct, for each $0<\alpha <Q$, an $\alpha$-regular subspace. As an application, we give an alternative simple proof of the existence of $\alpha$-regular subspaces of a $Q$-dimensional complete Ahlfors regular metric space $(X,\rho )$, which was proved in \cite{JJKRRS}.

10 pages, 2 figures

References in corpus (1)

• Packing dimension and Ahlfors regularity of porous sets in metric spaces

Cited by in corpus (1)

• Dvoretzky-type theorem for Ahlfors regular spaces