{"paper":{"title":"The Ext group in the categories of topological abelian groups and topological vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Hugo J. Bello","submitted_at":"2016-03-07T14:45:29Z","abstract_excerpt":"This paper is devoted to the study of the group ${\\rm Ext} (G,H)$ of all extensions of topological abelian groups $0\\to H\\to X\\to G\\to 0$ and the group ${\\rm Ext}_{TVS} (Z,Y)$ of all extensions of topological vector spaces $0\\to Y\\to X\\to Z\\to 0$. We focus on their behaviour under taking products, countable coproducts, dense subgroups and open subgroups. Finally, we apply the obtained properties to formulate in a more general setting some known results in the category of locally compact abelian groups and to determine conditions in which being a topological vector space is a three space proper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02091","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"}