2021
DOI: 10.48550/arxiv.2110.08929
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Universal spaces for asymptotic dimension zero

Abstract: Contents 1. Introduction 1 2. Preliminaries 2 3. Coarse disjoint unions 3 4. Special ultrametric spaces 5 5. Universal spaces 6 6. Ultrametric groups as universal spaces 7 References 9Abstract. Dranishnikov and Zarichnyi constructed a universal space in the coarse category of spaces of bounded geometry of asymptotic dimension 0. In this paper we construct universal spaces in the coarse category of separable (respectively, proper) metric spaces of asymptotic dimension 0. Our methods provide an alternative proof… Show more

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“…Note that universal spaces for 0-dimensional spaces of bounded geometry and 0dimensional proper spaces were constructed in [2] and [3].…”
Section: Introductionmentioning
confidence: 99%
“…Note that universal spaces for 0-dimensional spaces of bounded geometry and 0dimensional proper spaces were constructed in [2] and [3].…”
Section: Introductionmentioning
confidence: 99%