{"paper":{"title":"Totally Disconnected Semigroup Compactifications: Non-Introversion of the Full Boolean Algebra of Clopen Sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.GR"],"primary_cat":"math.GN","authors_text":"Emily Thevenot, Joshua Basman Monterrubio, Ross Stokke, Thomas Czyzowicz","submitted_at":"2026-06-22T22:36:03Z","abstract_excerpt":"In terms of the existence of a single clopen set and two related nets, we characterize when the full Boolean algebra, ${\\mathfrak B}(G)$, of clopen subsets of a topological group $G$ is left introverted. We employ this characterization to show that when $G$ is a first countable, $\\sigma$-compact, totally disconnected locally compact group, ${\\mathfrak B}(G)$ is left introverted if and only if $G$ is compact or discrete, thus providing a strong positive answer to a question posed in Stephens and Stokke (Q J Math 2023). Examples of clopen sets and nets witnessing our non-introversion theorem are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23987","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/2606.23987/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"}