{"paper":{"title":"The comb-like representations of cellular ordinal balleans","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"I.V. Protasov, K.D. Protasova","submitted_at":"2016-03-29T10:28:53Z","abstract_excerpt":"Given two ordinal $\\lambda$ and $\\gamma$, let $f:[0,\\lambda) \\rightarrow [0,\\gamma)$ be a function such that, for each $\\alpha<\\gamma$, $\\sup\\{f(t): t\\in[0, \\alpha]\\}<\\gamma.$ We define a mapping $d_{f}: [0,\\lambda)\\times [0,\\lambda) \\longrightarrow [0,\\gamma)$ by the rule: if $x<y$ then $d_{f}(x,y)= d_{f}(y,x)= \\sup\\{f(t): t\\in(x,y]\\}$, $d(x,x)=0$. The pair $([0,\\lambda), d_{f})$ is called a $\\gamma-$comb defined by $f$. We show that each cellular ordinal ballean can be represented as a $\\gamma-$comb. In {\\it General Asymptology}, cellular ordinal balleans play a part of ultrametric spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08713","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"}