{"paper":{"title":"On the reflection of the countable chain condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ramiro de la Vega","submitted_at":"2018-04-24T15:41:30Z","abstract_excerpt":"We study the question of when an uncountable ccc topological space $X$ contains a ccc subspace of size $\\aleph_1$. We show that it does if $X$ is compact Hausdorff and more generally if $X$ is Hausdorff with $\\mathrm{pct}(X) \\leq \\aleph_1$. For each regular cardinal $\\kappa$, an example is constructed of a ccc Tychonoff space of size $\\kappa$ and countable pseudocharacter but with no ccc subspace of size less than $\\kappa$. We also give a ccc compact $T_1$ space of size $\\kappa$ with no ccc subspace of size less than $\\kappa$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09103","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"}