{"paper":{"title":"A note on Collins-Roscoe Structuring Mechanism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ziqin Feng","submitted_at":"2014-08-19T19:32:14Z","abstract_excerpt":"A space $X$ has countable $(F)$-property if it has countable point network satisfying the Collins-Roscoe structuring mechanism. Some sufficient conditions for $C_p(X)$ having countable $(F)$-property are obtained. As a corollary, we prove that if $X$ is Corson compact, $C_p(X)$ satisfies countable $(F)$. This answers a question raised by Tkachuk. Also we get a class of function spaces with hereditarily $D$-property. We also prove that the countable $(F)$-property is preserved by taking $\\Sigma_s$-product. This answers questions of Tkachuk positively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4436","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"}