{"paper":{"title":"Classifying homogeneous cellular ordinal balleans up to coarse equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GN","authors_text":"Dusan Repovs, Igor Protasov, Sergii Slobodianiuk, Taras Banakh","submitted_at":"2014-09-13T04:50:16Z","abstract_excerpt":"For every ballean $X$ we introduce two cardinal characteristics $cov^\\flat(X)$ and $cov^\\sharp(X)$ describing the capacity of balls in $X$. We observe that these cardinal characteristics are invariant under coarse equivalence and prove that two cellular ordinal balleans $X,Y$ are coarsely equivalent if $cof(X)=cof(Y)$ and $cov^\\flat(X)=cov^\\sharp(X)=cov^\\flat(Y)=cov^\\sharp(Y)$. This result implies that a cellular ordinal ballean $X$ is homogeneous if and only if $cov^\\flat(X)=cov^\\sharp(X)$. Moreover, two homogeneous cellular ordinal balleans $X,Y$ are coarsely equivalent if and only if $cof(X"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3910","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"}