{"paper":{"title":"Order topology on orthocomplemented posets of linear subspaces of a pre-Hilbert space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"David Buhagiar, Emmanuel Chetcuti, Hans Weber","submitted_at":"2018-12-10T19:08:35Z","abstract_excerpt":"Motivated by the Hilbert-space model for quantum mechanics, we define a pre-Hilbert space logic to be a pair $(S,\\el)$, where $S$ is a pre-Hilbert space and $\\el$ is an orthocomplemented poset of orthogonally closed linear subspaces of $S$, closed w.r.t. finite dimensional perturbations, (i.e. if $M\\in\\el$ and $F$ is a finite dimensional linear subspace of $S$, then $M+F\\in \\el$). We study the order topology $\\tau_o(\\el)$ on $\\el$ and show that completeness of $S$ can by characterized by the separation properties of the topological space $(\\el,\\tau_o(\\el))$. It will be seen that the remarkable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04029","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"}