Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658479 | Topology and its Applications | 2014 | 8 Pages |
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 [4].We study asymptotic dimension with linear control ℓ-asdimωℓ-asdimω that depends on a fixed ultrafilter ω on NN. It turns out that the asymptotic Assouad–Nagata dimension is the supremum of ℓ-asdimωℓ-asdimω over all ω and the asymptotic dimension with linear control is the minimum of ℓ-asdimωℓ-asdimω over all ω.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Corry M. Bedwell,