{"paper":{"title":"Extensions of topological Abelian groups and three-space problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Hugo J. Bello, Mar\\'ia Jes\\'us Chasco, Xabier Dom\\'inguez","submitted_at":"2013-05-20T13:04:17Z","abstract_excerpt":"A twisted sum in the category of topological abelian groups is a short exact sequence $0\\to Y\\to X \\to Z\\to 0$ where all maps are assumed to be continuous and open onto their images. The twisted sum splits if it is equivalent to $0\\to Y\\to Y \\times Z \\to Z\\to 0$. \\par We study the class $\\ST$ of topological groups $G$ for which every twisted sum $0\\to \\T\\to X \\to G\\to 0$ splits. We prove that this class contains locally precompact groups, sequential direct limits of locally compact groups and topological groups with $\\mathcal{L}_\\infty$ topologies. We also prove that it is closed by taking ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4515","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":""},"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"}