{"paper":{"title":"Uniform boundedness of pretangent spaces and local strong one-side porosity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.MG","authors_text":"Oleksiy Dovgoshey, Viktoriia Bilet","submitted_at":"2013-02-19T13:07:41Z","abstract_excerpt":"Let (X,d,p) be a pointed metric space. A pretangent space to X at p is a metric space consisting of some equivalence classes of convergent to p sequences (x_n), x_n \\in X, whose degree of convergence is comparable with a given scaling sequence (r_n), r_n\\downarrow 0. We say that (r_n) is normal if there is (x_n) such that |d(x_n,p)-r_n|=o(r_n) for n\\to\\infty. Let Omega_{p}^{X}(n) be the set of pretangent spaces to X at p with normal scaling sequences. We prove that the spaces from Omega_{p}^{X}(n) are uniformly bounded if and only if {d(x,p:x\\in X}is a so-called completely strongly porous set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4599","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"}