{"paper":{"title":"On the $C_k$-stable closure of the class of (separable) metrizable spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Saak Gabriyelyan, Taras Banakh","submitted_at":"2014-12-06T10:23:36Z","abstract_excerpt":"Denote by $\\mathbf C_k[\\mathfrak M]$ the $C_k$-stable closure of the class $\\mathfrak M$ of all metrizable spaces, i.e., $\\mathbf C_k[\\mathfrak M]$ is the smallest class of topological spaces that contains $\\mathfrak M$ and is closed under taking subspaces, homeomorphic images, countable topological sums, countable Tychonoff products, and function spaces $C_k(X,Y)$ with Lindel\\\"of domain. We show that the class $\\mathbf C_k[\\mathfrak M]$ coincides with the class of all topological spaces homeomorphic to subspaces of the function spaces $C_k(X,Y)$ with a separable metrizable space $X$ and a met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2216","kind":"arxiv","version":3},"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"}