{"paper":{"title":"Asymptotic structure of general metric spaces at infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Oleksiy Dovgoshey, Viktoriia Bilet","submitted_at":"2017-08-17T12:39:12Z","abstract_excerpt":"Let $(X,d)$ be an unbounded metric space and $\\tilde r=(r_n)_{n\\in\\mathbb N}$ be a scaling sequence of positive real numbers tending to infinity. We define the pretangent space $\\Omega_{\\infty, \\tilde r}^{X}$ to $(X, d)$ at infinity as a metric space whose points are equivalence classes of sequences $(x_n)_{n\\in\\mathbb N}\\subset X$ which tend to infinity with the speed of $\\tilde r$. It is proved that the pretangent spaces $\\Omega_{\\infty, \\tilde r}^{X}$ are complete for every unbounded metric space $(X, d)$ and every scaling sequence $\\tilde r$. The finiteness conditions of $\\Omega_{\\infty, \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05235","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"}