{"paper":{"title":"Relative Computability and Uniform Continuity of Relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"Arno Pauly, Martin Ziegler","submitted_at":"2011-05-16T10:06:40Z","abstract_excerpt":"A type-2 computable real function is necessarily continuous; and this remains true for relative, i.e. oracle-based computations. Conversely, by the Weierstrass Approximation Theorem, every continuous f:[0,1]->R is computable relative to some oracle.\n  In their search for a similar topological characterization of relatively computable multivalued functions f:[0,1]=>R (aka relations), Brattka and Hertling (1994) have considered two notions: weak continuity (which is weaker than relative computability) and strong continuity (which is stronger than relative computability). Observing that uniform c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3050","kind":"arxiv","version":2},"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"}