{"paper":{"title":"On monomorphic topological functors with finite supports","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.GT"],"primary_cat":"math.CT","authors_text":"Marta Martynenko, Michael Zarichnyi, Taras Banakh","submitted_at":"2010-04-03T16:53:04Z","abstract_excerpt":"We prove that a monomorphic functor $F:Comp\\to Comp$ with finite supports is epimorphic, continuous, and its maximal $\\emptyset$-modification $F^\\circ$ preserves intersections. This implies that a monomorphic functor $F:Comp\\to Comp$ of finite degree $deg F\\le n$ preserves (finite-dimensional) compact ANR's if the spaces $F\\emptyset$, $F^\\circ\\emptyset$, and $Fn$ are finite-dimensional ANR's. This improves a known result of Basmanov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0457","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"}