{"paper":{"title":"On the tightness of $G_\\delta$-modifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Alan Dow, Istv\\'an Juh\\'asz, Lajos Soukup, William Weiss, Zolt\\'an Szentmikl\\'ossy","submitted_at":"2018-05-06T15:12:55Z","abstract_excerpt":"The $G_\\delta$-modification $X_\\delta$ of a topological space $X$ is the space on the same underlying set generated by, i.e. having as a basis, the collection of all $G_\\delta$ subsets of $X$. Bella and Spadaro recently investigated the connection between the values of various cardinal functions taken on $X$ and $X_\\delta$, respectively. In their paper, as Question 2, they raised the following problem: Is $t(X_\\delta) \\le 2^{t(X)}$ true for every (compact) $T_2$ space $X$? Note that this is actually two questions.\n  In this note we answer both questions: In the compact case affirmatively and i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02228","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"}