{"paper":{"title":"Linear continuous surjections of $C_{p}$-spaces over compacta","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Arkady Leiderman, Kazuhiro Kawamura","submitted_at":"2016-05-17T18:15:30Z","abstract_excerpt":"Let $X$ and $Y$ be compact Hausdorff spaces and suppose that there exists a linear continuous surjection $T:C_{p}(X) \\to C_{p}(Y)$, where $C_{p}(X)$ denotes the space of all real-valued continuous functions on $X$ endowed with the pointwise convergence topology. We prove that $\\dim X=0$ implies $\\dim Y = 0$. This generalizes a previous theorem \\cite[Theorem 3.4]{LLP} for compact metrizable spaces. Also we point out that the function space $C_{p}(P)$ over the pseudo-arc $P$ admits no densely defined linear continuous operator $C_{p}(P) \\to C_{p}([0,1])$ with a dense image."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05276","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"}