{"paper":{"title":"From Freudenthal's Spectral Theorem to projectable hulls of unital Archimedean lattice-groups, through compactifications of minimal spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.GR","math.SP"],"primary_cat":"math.FA","authors_text":"Andrea Pedrini, Daniel McNeill, Richard N. Ball, Vincenzo Marra","submitted_at":"2014-06-12T08:51:53Z","abstract_excerpt":"We use a landmark result in the theory of Riesz spaces - Freudenthal's 1936 Spectral Theorem - to canonically represent any Archimedean lattice-ordered group $G$ with a strong unit as a (non-separating) lattice-group of real valued continuous functions on an appropriate $G$-indexed zero-dimensional compactification $w_GZ_G$ of its space $Z_G$ of \\emph{minimal} prime ideals. The two further ingredients needed to establish this representation are the Yosida representation of $G$ on its space $X_G$ of \\emph{maximal} ideals, and the well-known continuous surjection of $Z_G$ onto $X_G$. We then est"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3152","kind":"arxiv","version":2},"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"}