{"paper":{"title":"On stable Baire classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Olena Karlova, Volodymyr Mykhaylyuk","submitted_at":"2015-12-06T07:33:30Z","abstract_excerpt":"We introduce and study adhesive spaces. Using this concept we obtain a characterization of stable Baire maps $f:X\\to Y$ of the class $\\alpha$ for wide classes of topological spaces. In particular, we prove that for a topological space $X$ and a contractible space $Y$ a map $f:X\\to Y$ belongs to the $n$'th stable Baire class if and only if there exist a sequence $(f_k)_{k=1}^\\infty$ of continuous maps $f_k:X\\to Y$ and a sequence $(F_k)_{k=1}^\\infty$ of functionally ambiguous sets of the $n$'th class in $X$ such that $f|_{F_k}=f_k|_{F_k}$ for every $k$. Moreover, we show that every monotone func"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01754","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"}