{"paper":{"title":"On $\\frac\\pi2$-separated subsets of Alexandrov spaces with curvature $\\geq1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hongwei Sun, Xiaole Su, Yusheng Wang","submitted_at":"2014-03-13T06:22:45Z","abstract_excerpt":"Let $M$ be an $n$-dimensional Alexandrov space with curvature $\\geq 1$, and let $\\{q_1,\\cdots,q_k\\}$ be any $\\frac\\pi2$-separated subset in $M$ (i.e. the distance $|q_iq_j|\\geq\\frac{\\pi}{2}$ for any $i\\neq j$). Under the additional conditions \"$|q_iq_j|<\\pi$\" and \"the diameter $\\diam(M)\\leq \\frac\\pi2$\", we respectively give the upper bound of $k$ (which depends only on $n$), and we classify the (topological or geometric) structure of $M$ when $k$ attains the upper bound."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3169","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"}