Remarks on coarse triviality of asymptotic Assouad-Nagata dimension

Abstract

We show for a given metric space $(X,d)$ of asymptotic dimension $n$ that there exists a coarsely and topologically equivalent hyperbolic metric $d^{\prime }$ of the form $d^{\prime }=f\circ d$ such that $(X,d^{\prime })$ is of asymptotic Assouad-Nagata dimension $n$. As a corollary we construct examples of spaces realising strict inequality in the logarithmic law for AN-asdim of a Cartesian product. One of them may be viewed as a counterexample to a specific kind of a Morita-type theorem for AN-asdim.

A superfluous step in the proof of 1.4 removed, remarks about earlier results updated, a reference to the BSc thesis added, minor corrections

References in corpus (2)

• Hurewicz Theorem for Assouad-Nagata dimension
• Dimension of locally and asymptotically self-similar spaces

Cited by in corpus (1)

• Warped cones, (non-)rigidity, and piecewise properties, with a joint appendix with Dawid Kielak