{"paper":{"title":"Truncated Abelian Lattice-Ordered Groups II: the Pointfree (Madden) Representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.GN","authors_text":"Richard N. Ball","submitted_at":"2014-06-29T01:36:33Z","abstract_excerpt":"This is the second of three articles on the topic of truncation as an operation on divisible abelian lattice-ordered groups, or simply $\\ell$-groups. This article uses the notation and terminology of the first article and assumes its results. In particular, we refer to an $\\ell$-group with truncation as a truncated $\\ell$-group, or simply a trunc, and denote the category of truncs with truncation morphisms by $\\mathbf{AT}$.\n  Here we develop the analog for $\\mathbf{AT}$ of Madden's pointfree representation for $\\mathbf{W}$, the category of archimedean $\\ell$-groups with designated order unit. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7454","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"}