{"paper":{"title":"Interpolation sets in spaces of continuous metric-valued functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Luis T\\'arrega, Mar\\'ia V. Ferrer, Salvador Hern\\'andez","submitted_at":"2017-07-20T14:50:15Z","abstract_excerpt":"Let $X$ and $M$ be a topological space and metric space, respectively. If $C(X,M)$ denotes the set of all continuous functions from X to M, we say that a subset $Y$ of $X$ is an \\emph{$M$-interpolation set} if given any function $g\\in M^Y$ with relatively compact range in $M$, there exists a map $f\\in C(X,M)$ such that $f_{|Y}=g$. In this paper, motivated by a result of Bourgain in \\cite{Bourgain1977}, we introduce a property, stronger than the mere \\emph{non equicontinuity} of a family of continuous functions, that isolates a crucial fact for the existence of interpolation sets in fairly gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06550","kind":"arxiv","version":2},"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"}