{"paper":{"title":"Spaces with a $\\mathbb{Q}$-diagonal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ziqin Feng","submitted_at":"2017-09-20T14:14:31Z","abstract_excerpt":"A space $X$ has a $\\mathbb{Q}$-diagonal if $X^2\\setminus \\Delta$ has a $\\mathcal{K}(\\mathbb{Q})$-directed compact cover. We show that any compact space with a $\\mathbb{Q}$-diagonal is metrizable, hence any Tychonorff space with a $\\mathbb{Q}$-diagonal is cosmic. These give a positive answer to Problem 4.2 and Problem 4.8 in \\cite{COT11} raised by Cascales, Orihuela and Tkachuk."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06879","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"}