{"paper":{"title":"On recurrence in G-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Igor Protasov, Ksenia Protasova","submitted_at":"2017-03-02T10:09:58Z","abstract_excerpt":"We introduce and analyze the following general concept of recurrence. Let $G$ be a group and let $X$ be a G-space with the action $G\\times X\\longrightarrow X$, $(g,x)\\longmapsto gx$. For a family $\\mathfrak{F}$ of subset of $X$ and $A\\in \\mathfrak{F}$, we denote $\\Delta_{\\mathfrak{F}}(A)=\\{g\\in G: gB\\subseteq A$ for some $B\\in \\mathfrak{F}, \\ B\\subseteq A\\}$, and say that a subset $R$ of $G$ is $\\mathfrak{F}$-recurrent if $R\\bigcap \\Delta_{\\mathfrak{F}} (A)\\neq\\emptyset$ for each $A\\in \\mathfrak{F}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00695","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"}