Universal spaces for asymptotic dimension
A. Dranishnikov, M. Zarichnyi
TL;DR
This paper constructs a universal space for proper metric spaces with bounded geometry and fixed asymptotic dimension, and proves the equivalence of asymptotic and asymptotic inductive dimensions.
Contribution
It introduces a universal space for proper metric spaces of bounded geometry with a specified asymptotic dimension, linking different dimension concepts.
Findings
Universal space construction for proper metric spaces with fixed asymptotic dimension
Proves asymptotic dimension equals asymptotic inductive dimension
Establishes foundational connection between different dimension notions
Abstract
We construct a universal space for the class of proper metric spaces of bounded geometry and of given asymptotic dimension. As a consequence of this result, we establish coincidence of the asymptotic dimension with the asymptotic inductive dimensions.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Holomorphic and Operator Theory · Advanced Algebra and Geometry