{"paper":{"title":"Continuous images of Cantor's ternary set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.DS","authors_text":"Fabian Dreher, Tony Samuel","submitted_at":"2013-03-15T15:37:22Z","abstract_excerpt":"The Hausdorff-Alexandroff Theorem states that any compact metric space is the continuous image of Cantor's ternary set $C$. It is well known that there are compact Hausdorff spaces of cardinality equal to that of $C$ that are not continuous images of Cantor's ternary set. On the other hand, every compact countably infinite Hausdorff space is a continuous image of $C$. Here we present a compact countably infinite non-Hausdorff space which is not the continuous image of Cantor's ternary set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3810","kind":"arxiv","version":2},"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"}