{"paper":{"title":"Computable dyadic subbases and $\\mathbf{T}^\\omega$-representations of compact sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Arno Pauly, Hideki Tsuiki","submitted_at":"2016-04-01T14:24:02Z","abstract_excerpt":"We explore representing the compact subsets of a given represented space by infinite sequences over Plotkin's $\\mathbb{T}$. We show that computably compact computable metric spaces admit representations of their compact subsets in such a way that compact sets are essentially underspecified points. We can even ensure that a name of an $n$-element compact set contains $n$ occurrences of $\\bot$. We undergo this study effectively and show that such a $\\mathbb{T}^\\omega$-representation is effectively obtained from structures of computably compact computable metric spaces. As an application, we prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00258","kind":"arxiv","version":3},"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"}