{"paper":{"title":"Characterizations of Faces of Convex Sets in Infinite-dimensional Vector Spaces","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Valentin V. Gorokhovik","submitted_at":"2025-06-10T12:38:08Z","abstract_excerpt":"In the paper three different characterizations of faces of convex sets, belonging to infinite-dimensional real vector spaces, are presented. The first one is formulated in the terms of generalized semispaces, the second -- in the terms of compatible complete (total) preorders, and the third -- in the terms of step-affine functions. All three characterization are equivalent each other and extend to infinite-dimensional vector spaces the lexicographical characterization of faces established in finite-dimensional settings by Martinez-Legaz J.-E. (Acta Mathematica Vietnamica. 1997. Vol. 22, No.~1,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08742","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.08742/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}