{"paper":{"title":"Balleans, hyperballeans and ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"D. Dikranjan, I. Protasov, K. Protasova, N. Zava","submitted_at":"2019-02-04T21:46:28Z","abstract_excerpt":"A ballean $\\mathcal{B}$ (or a coarse structure) on a set $X$ is a family of subsets of $X$ called balls (or entourages of the diagonal in $X\\times X$) defined in such a way that $\\mathcal{B}$ can be considered as the asymptotic counterpart of a uniform topological space. The aim of this paper is to study two concrete balleans defined by the ideals in the Boolean algebra of all subsets of $X$ and their hyperballeans, with particular emphasis on their connectedness structure, more specifically the number of their connected components."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01469","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"}