{"paper":{"title":"On character of points in the Higson corona of a metric space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GN","authors_text":"Lubomyr Zdomskyy, Ostap Chervak, Taras Banakh","submitted_at":"2012-06-04T14:00:37Z","abstract_excerpt":"We prove that for an unbounded metric space $X$, the minimal character $m\\chi(\\check X)$ of a point of the Higson corona $\\check X$ of $X$ is equal to $\\mathfrak u$ if $X$ has asymptotically isolated balls and to $\\max\\{\\mathfrak u,\\mathfrak d\\}$ otherwise. This implies that under $\\mathfrak u<\\mathfrak d$ a metric space $X$ of bounded geometry is coarsely equivalent to the Cantor macro-cube $2^{<\\IN}$ if and only if $\\dim(\\check X)=0$ and $m\\chi(\\check X)=\\mathfrak d$. This contrasts with a result of Protasov saying that under CH the coronas of any two asymptotically zero-dimensional unbounde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0626","kind":"arxiv","version":1},"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"}