{"paper":{"title":"Locally uniformly rotund renormings of the spaces of continuous functions on Fedorchuk compacts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. V. Ivanov, M. S. Shulikina, S. P. Gul'ko, S. Troyanski","submitted_at":"2018-11-22T15:09:56Z","abstract_excerpt":"We show that $C(X)$ admits an equivalent pointwise lower semicontinuous locally uniformly rotund norm provided $X$ is Fedorchuk compact of spectral height 3. In other words $X$ admits a fully closed map $f$ onto a metric compact $Y$ such that $f^{-1}(y)$ is metrizable for all $y\\in Y$ . A continuous map of compacts $f : X \\to Y$ is said to be fully closed if for any disjoint closed subsets $A;B \\subset X$ the intersection $f(A) \\cap f(B)$ is finite. For instance the projection of the lexicographic square onto the first factor is fully closed and all its fibers are homeomorphic to the closed in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09200","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"}