{"paper":{"title":"Products of topological groups in which all closed subgroups are separable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Arkady G. Leiderman, Mikhail G. Tkachenko","submitted_at":"2016-12-31T10:51:14Z","abstract_excerpt":"We prove that if $H$ is a topological group such that all closed subgroups of $H$ are separable, then the product $G\\times H$ has the same property for every separable compact group $G$.\n  Let $c$ be the cardinality of the continuum. Assuming $2^{\\omega_1} = c$, we show that there exist:\n  (1) pseudocompact topological abelian groups $G$ and $H$ such that all closed subgroups of $G$ and $H$ are separable, but the product $G\\times H$ contains a closed non-separable $\\sigma$-compact subgroup;\n  (2) pseudocomplete locally convex vector spaces $K$ and $L$ such that all closed vector subspaces of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00084","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"}