{"paper":{"title":"An inductive proof of the Feinstein-Heath Swiss cheese \"classicalisation\" theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jonathan Mason","submitted_at":"2010-10-12T23:32:04Z","abstract_excerpt":"A theory of allocation maps has been developed by J. F. Feinstein and M. J. Heath in order to prove a theorem, using Zorn's lemma, concerning the compact plane sets known as Swiss cheese sets. These sets are important since, as domains, they provide a good source of examples in the theory of uniform algebras and rational approximation. In this paper we take a more direct approach when proving their theorem by using transfinite induction and cardinality. An explicit reference to a theory of allocation maps is no longer required. Instead we find that the repeated application of a single operatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2537","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"}