{"paper":{"title":"Universal nowhere dense and meager sets in Menger manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GT","authors_text":"Dusan Repovs, Taras Banakh","submitted_at":"2013-02-22T17:34:24Z","abstract_excerpt":"In each Menger manifold $M$ we construct: (i) a closed nowhere dense subset $M_0$ which is homeomorphic to $M$ and is universal nowhere dense in the sense that for each nowhere dense set $A\\subset M$ there is a homeomorphism $h$ of $M$ such that $h(A)\\subset M_0$; (ii) a meager $F_\\sigma$-set $\\Sigma_0\\subset M$ which is universal meager in the sense that for each meager subset $B\\subset M$ there is a homeomorphism $h$ of $M$ such that $h(B)\\subset \\Sigma_0$.\n  Also we prove that any two universal meager $F_\\sigma$-sets in $M$ are ambiently homeomorphic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5656","kind":"arxiv","version":2},"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"}