{"paper":{"title":"Szlenk and $w^*$-dentability indices of $C(K)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ryan M Causey","submitted_at":"2016-05-06T15:21:39Z","abstract_excerpt":"Given any compact, Hausdorff space $K$ and $1<p<\\infty$, we compute the Szlenk and $w^*$-dentability indices of the spaces $C(K)$ and $L_p(C(K))$. We show that if $K$ is compact, Hausdorff, scattered, $CB(K)$ is the Cantor-Bendixson index of $K$, and $\\xi$ is the minimum ordinal such that $CB(K)\\leqslant \\omega^\\xi$, then $Sz(C(K))=\\omega^\\xi$ and $Dz(C(K))=Sz(L_p(C(K)))= \\omega^{1+\\xi}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01969","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"}