{"paper":{"title":"A coarse characterization of the Baire macro-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"Ihor Zarichnyi, Taras Banakh","submitted_at":"2011-03-26T08:52:53Z","abstract_excerpt":"We prove that each coarsely homogenous separable metric space $X$ is coarsely equivalent to one of the spaces: the sigleton, the Cantor macro-cube or the Baire macro-space. This classification is derived from coarse characterizations of the Cantor macro-cube and of the Baire macro-space given in this paper. Namely, we prove that a separable metric space $X$ is coarsely equivalent to the Baire macro-space if any only if $X$ has asymptotic dimension zero and has unbounded geometry in the sense that for every $\\delta$ there is $\\epsilon$ such that no $\\epsilon$-ball in $X$ can be covered by finit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5118","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}