{"paper":{"title":"Weak split extensions of topological Abelian groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT","math.GR"],"primary_cat":"math.AT","authors_text":"Luis Javier Hern\\'andez-Paricio, Mar\\'ia V. Ferrer, Salvador Hern\\'andez-Mu\\~noz","submitted_at":"2026-06-06T09:34:08Z","abstract_excerpt":"In the category of topological Abelian groups, we consider the usual notion of an extension $E=(B \\to X \\to A)$ of $B$ by $A$, together with the notion of a weakly split extension, i.e., an extension for which the projection $X \\to A$ admits a continuous section $A \\to X$. Given a weakly split extension $E$, the topological Abelian group $X$ is homeomorphic to $B \\times A$, although in general it is not algebraically isomorphic to $B \\times A$.\n  For two topological Abelian groups $A$ and $B$, we study the Abelian group $E^{\\mathrm{ws}}_{\\mathrm{TA}}(A,B)$ of weakly split extensions of $B$ by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08069","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/2606.08069/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"}