{"paper":{"title":"Cofinal types of topological groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR","math.LO"],"primary_cat":"math.GN","authors_text":"Dekui Peng, Xuan Gong","submitted_at":"2026-05-25T05:49:59Z","abstract_excerpt":"We investigate the local topological structure of non-metrizable topological groups through the lens of Tukey order and cofinal types. Motivated by recent advances in topological groups admitting an $\\omega^\\omega$-base, we introduce the \\emph{fineness index}, denoted $\\f(P)$, for arbitrary directed partially ordered sets. This cardinal invariant fundamentally generalizes the bounding number $\\mathfrak{b}$ by capturing the exact threshold where a poset evades domination by its countable subsets, thereby establishing a universal lower bound for the character of topological groups with a $P$-bas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25445","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25445/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}