{"paper":{"title":"Partitions of 2^{\\omega} and completely ultrametrizable spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Arnold W. Miller, William R. Brian","submitted_at":"2014-06-05T14:48:46Z","abstract_excerpt":"We prove that, for every n, the topological space {\\omega}_n^{\\omega} (where {\\omega}_n has the discrete topology) can be partitioned into {\\omega}_n copies of the Baire space. Using this fact, the authors then prove two new theorems about completely ultrametrizable spaces. We say that Y is a condensation of X if there is a continuous bijection from X to Y. First, it is proved that the Baire space is a condensation of {\\omega}_n^{\\omega} if and only if it can be partitioned into {\\omega}_n Borel sets, and some consistency results are given regarding such partitions. It is also proved that it i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1405","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"}