{"paper":{"title":"Countable Dense Homogeneity and the Double Arrow Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Rodrigo Hern\\'andez-Guti\\'errez","submitted_at":"2018-09-18T16:24:43Z","abstract_excerpt":"Let $\\mathbb{A}$ denote the Alexandroff-Urysohn double arrow space. We prove the following results: (a) $\\mathbb{A}\\times{}^\\omega{2}$ is not countable dense homogeneous; (b) ${}^{\\omega}{\\mathbb{A}}$ is not countable dense homogeneous; (c) $\\mathbb{A}$ has exactly $\\mathfrak{c}$ types of countable dense subsets. These results answer questions by Arhangel'ski\\u\\i, Hru\\v{s}\\'ak and van Mill."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06816","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"}