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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 $"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.00084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-12-31T10:51:14Z","cross_cats_sorted":[],"title_canon_sha256":"f8fb7e4255edf7ab90fdf12a9d40201e42140cfaab2b3dcc9bd7f58a4a8e0d61","abstract_canon_sha256":"ad963355ab611eb2cb1e9ad958222c09a2cfaf688776ab78b7c8fa73ce516e13"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:39.454979Z","signature_b64":"yK5fV+dt4JbeNpq9qOh1vOCfGkBWn8ApCqwhAIYwrdVg17RXqBwbWR/XPHfXBBHSjG4zaQLOvtCQTKoZ0pO6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91df4eded8ce21c57be7d1d3f9d8c3d3d7e62663cacf1b636eaaef94a640b95f","last_reissued_at":"2026-05-18T00:53:39.454568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:39.454568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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