{"paper":{"title":"A Remark on Two Extensions of the Disc Algebra and Mergelyan's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"I. Papadoperakis, V. Nestoridis","submitted_at":"2011-04-05T13:11:41Z","abstract_excerpt":"We investigate the set of uniform limits of polynomials on any closed Jordan domain with respect to the chordal metric $\\chi$ on $\\mathbb{C}\\cup\\{\\infty \\}$. We conclude that Mergelyan's Theorem may be extended to the case of uniform approximation with respect to $\\chi$ on closed Jordan domains. Similar results are obtained if we replace the one point compactification $\\mathbb{C}\\cup\\{\\infty\\}$ of $\\mathbb{C}$ by another compactification of $\\mathbb{C}$ homeomorphic to the closed unit disc."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0833","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"}