{"paper":{"title":"On the Borel Complexity of Characterized Subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Daniele Impieri, Dikran Dikranjan","submitted_at":"2014-12-09T13:12:18Z","abstract_excerpt":"In a compact abelian group $X$, a characterized subgroup is a subgroup $H$ such that there exists a sequence of characters $\\vs=(v_n)$ of $X$ such that $H=\\{x\\in X:v_n(x)\\to 0 \\text{ in } \\T\\}$. Gabriyelyan proved for $X=\\T$, that $\\{x\\in\\T:n!x\\to 0 \\text{ in }\\T\\}$ is not an $F_\\sigma$-set. In this paper, we give a complete description of the $F_\\sigma$-subgroups of $\\T$ characterized by sequences of integers $\\vs=(v_n)$ such that $v_n|v_{n+1}$ for all $n\\in\\N$ (we show that these are exactly the countable characterized subgroups). Moreover in the general setting of compact metrizable abelian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2949","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"}