{"paper":{"title":"Precompact abelian groups and topological annihilators","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"G\\'abor Luk\\'acs","submitted_at":"2005-02-10T23:37:16Z","abstract_excerpt":"For a compact Hausdorff abelian group K and its subgroup H, one defines the g-closure g(H) of H in K as the subgroup consisting of $\\chi \\in K$ such that $\\chi(a_n)\\longrightarrow 0$ in T=R/Z for every sequence {a_n} in $\\hat K$ (the Pontryagin dual of K) that converges to 0 in the topology that H induces on $\\hat K$. We prove that every countable subgroup of a compact Hausdorff group is g-closed, and thus give a positive answer to two problems of Dikranjan, Milan and Tonolo. We also show that every g-closed subgroup of a compact Hausdorff group is realcompact. The techniques developed in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502223","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"}