{"paper":{"title":"$G_\\delta$-topology and compact cardinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"Toshimichi Usuba","submitted_at":"2017-09-23T02:50:06Z","abstract_excerpt":"For a topological space $X$, let $X_\\delta$ be the space $X$ with $G_\\delta$-topology of $X$. For an uncountable cardinal $\\kappa$, we prove that the following are equivalent: (1) $\\kappa$ is $\\omega_1$-strongly compact. (2) For every compact Hausdorff space $X$, the Lindel\\\"of degree of $X_\\delta$ is $\\le \\kappa$. (3) For every compact Hausdorff space $X$, the weak Lindel\\\"of degree of $X_\\delta$ is $\\le \\kappa$. This shows that the least $\\omega_1$-strongly compact cardinal is the supremum of the Lindel\\\"of and the weak Lindel\\\"of degrees of compact Hausdorff spaces with $G_\\delta$-topology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07991","kind":"arxiv","version":4},"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"}