{"paper":{"title":"Ultracompanions of subsets of a group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"I. Protasov, S. Slobodianiuk","submitted_at":"2013-08-07T08:20:23Z","abstract_excerpt":"Let $G$ be a group, $\\beta G$ is the Stone-$\\check{C}$ech compactification of $\\beta G$ endowed with the structure of a right topological semigroup, $G^*=\\beta G\\setminus G$. Given any subset $A$ of $G$ and $p\\in G^*$, we define the $p$-companion $\\vt_p(A)=A^*\\cap Gp$ of $A$, and characterize the subsets with finite and discrete ultracompanions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1499","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"}