{"paper":{"title":"Mappings of preserving $n$-distance one in $n$-normed spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dongni Tan, Xujian Huang","submitted_at":"2016-09-20T06:40:18Z","abstract_excerpt":"We give a positive answer to the Aleksandrov problem in $n$-normed spaces under the surjectivity assumption. Namely, we show that every surjective mapping preserving $n$-distance one is affine, and thus is an $n$-isometry. This is the first time to solve the Aleksandrov problem in $n$-normed spaces with only surjective assumption even in the usual case $n=2$. Finally, when the target space is $n$-strictly convex, we prove that every mapping preserving two $n$-distances with an integer ratio is an affine $n$-isometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06033","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"}