{"paper":{"title":"Borel complexity of isometry classes of $\\mathcal{C}(K)$ spaces with countable compacta","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jakub Rondo\\v{s}, Marek C\\'uth, Martin Dole\\v{z}al, Ond\\v{r}ej Kurka","submitted_at":"2026-06-19T08:17:10Z","abstract_excerpt":"For every countable compact space $K$, we determine the exact Borel complexity of the isometry class of the Banach space $\\mathcal{C}(K)$. As a byproduct, we also determine the precise Borel complexity of the homeomorphism class of a fixed countable compact space $K$, improving earlier results of Cenzer and Mauldin. The above results provide concrete and natural examples of sets with arbitrarily high, still exactly determined, Borel complexity.\n  Moreover, we find a new characterization of those real $L_1$-preduals that are isometric to $\\mathcal{C}(K)$ for some zero-dimensional compact space "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21204","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.21204/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}