{"paper":{"title":"A characterization of injective subsets in R^n with maximum norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Dominic Descombes","submitted_at":"2015-10-14T16:05:11Z","abstract_excerpt":"We characterize all (absolute) 1-Lipschitz retracts Q of R^n with the maximum norm. Omitting two technical details, they coincide with the subsets written as the solution set of (at most) 2n inequalities like follows. For every coordinate i=1,...,n, there is a lower and an upper bound L,U : R^{n-1} -> R of 1-Lipschitz maps with L \\leq U and the inequalities read\n  L(x_1,...,x_{i-1},x_{i+1},...,x_n) \\leq x_i \\leq U(x_1,...,x_{i-1},x_{i+1},...,x_n)\n  These sets are also exactly the injective subsets; meaning those Q such that every 1-Lipschitz map A -> Q, defined on a subset A of a metric space "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04181","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"}