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We show that a closed subgroup $H$ of $X$ is $T$-characterized if and only if $H$ is a $G_\\delta$-subgroup of $X$ and the annihilator of $H$ admits a Hausdorff minimally almost periodic group topology. All closed subgroups of an infinite compact Abelian group $X$ are $T$-characterized if and only if $X$ is metrizable and connected. We prove that every compact Abelian group $X$ of in"},"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":"1502.02308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-08T21:40:42Z","cross_cats_sorted":[],"title_canon_sha256":"e33d1a9ba0d2181a82cb20c6811b90ae13c0141a9b64eec88e2dc4bcce2d1309","abstract_canon_sha256":"2610b8c804b85e38374866dc49bd0b86c9692b098fab170545e53039d964a018"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:42.915435Z","signature_b64":"VFjYm7oq6zuAM2MWGw9P1Btx5ArdnROM0F2603eCjPQrWcDKT2Le4eamjvqH+31aW69yXXn/RHVjcWjedKXOBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"415b72ee3e8d485f2e71a5b11e75768ce68ccc10bd28f589d9efb9407822a42a","last_reissued_at":"2026-05-18T02:27:42.914615Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:42.914615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $T$-characterized subgroups of compact Abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"S. Gabriyelyan","submitted_at":"2015-02-08T21:40:42Z","abstract_excerpt":"We say that a subgroup $H$ of an infinite compact Abelian group $X$ is {\\it $T$-characterized} if there is a $T$-sequence $\\mathbf{u} =\\{u_n \\}$ in the dual group of $X$ such that $H=\\{x\\in X: \\; (u_n, x)\\to 1 \\}$. We show that a closed subgroup $H$ of $X$ is $T$-characterized if and only if $H$ is a $G_\\delta$-subgroup of $X$ and the annihilator of $H$ admits a Hausdorff minimally almost periodic group topology. All closed subgroups of an infinite compact Abelian group $X$ are $T$-characterized if and only if $X$ is metrizable and connected. 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