{"paper":{"title":"Almost maximally almost-periodic group topologies determined by T-sequences","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"G\\'abor Luk\\'acs","submitted_at":"2005-03-31T23:33:44Z","abstract_excerpt":"A sequence $\\{a_n\\}$ in a group $G$ is a {\\em $T$-sequence} if there is a Hausdorff group topology $\\tau$ on $G$ such that $a_n\\stackrel\\tau\\longrightarrow 0$. In this paper, we provide several sufficient conditions for a sequence in an abelian group to be a $T$-sequence, and investigate special sequences in the Pr\\\"ufer groups $\\mathbb{Z}(p^\\infty)$. We show that for $p\\neq 2$, there is a Hausdorff group topology $\\tau$ on $\\mathbb{Z}(p^\\infty)$ that is determined by a $T$-sequence, which is close to being maximally almost-periodic--in other words, the von Neumann radical $\\mathbf{n}(\\mathbb{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504003","kind":"arxiv","version":3},"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"}