{"paper":{"title":"Divisibility in the Stone-\\v{C}ech compactification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Boris \\v{S}obot","submitted_at":"2014-10-24T18:53:43Z","abstract_excerpt":"After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-Cech compactification \\beta N, we establish some results about one of such extensions. This provides us with one possible divisibility relation on \\beta N and we introduce a few more, defined in a natural way. For some of them we find equivalent conditions for divisibility. Finally, we mention a few facts about prime and irreducible elements of (\\beta N, \\cdot). The motivation behind all this is to try to translate problems in number theory into \\beta N."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6778","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"}