{"paper":{"title":"On the subset Combinatorics of G-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Igor Protasov, Sergii Slobodianiuk","submitted_at":"2014-09-25T17:58:46Z","abstract_excerpt":"Let $G$ be a group and let $X$ be a transitive $G$-space. We classify the subsets of $X$ with respect to a translation invariant ideal $\\mathcal{J}$ in the Boolean algebra of all subsets of $X$, introduce and apply the relative combinatorical derivations of subsets of $X$. Using the standard action of $G$ on the Stone-$\\check{C}$ech compactification $\\beta X$ of the discrete space $X$, we characterize the points $p\\in\\beta X$ isolated in $Gp$ and describe a size of a subset of $X$ in terms of its ultracompanions in $\\beta X$. We introduce and characterize scattered and sparse subsets of $X$ fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7350","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"}