On Asymptotic Dimension With Linear Control

Abstract

We construct a countable p-local group with a proper invariant metric whose Assouad-Nagata dimension is strictly greater than the asymptotic dimension with linear control. This solves Problem 8.6 from the list [Dr]. We study asymptotic dimension with linear control $\ell$-$asdi{m}_{\omega }$ that depends on a fixed ultrafilter on the naturals. It turns out that the Assouad-Nagata dimension is the supremum of $\ell$-$asdi{m}_{\omega }$ on all $\omega$ and the asymptotic dimension with linear control is the minimum.

References in corpus (1)

• Hurewicz Theorem for Assouad-Nagata dimension