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 -asdimω that depends on a fixed ultrafilter on the naturals. It turns out that the Assouad-Nagata dimension is the supremum of -asdimω on all ω and the asymptotic dimension with linear control is the minimum.
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