{"paper":{"title":"The continuity properties of compact-preserving functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Artur Bartoszewicz, Marek Bienias, Szymon Glab, Taras Banakh","submitted_at":"2012-08-11T07:50:57Z","abstract_excerpt":"A function $f:X\\to Y$ between topological spaces is called {\\em compact-preserving} if the image $f(K)$ of each compact subset $K\\subset X$ is compact. We prove that a function $f:X\\to Y$ defined on a strong Frechet space $X$ is compact-preserving if and only if for each point $x\\in X$ there is a compact subset $K_x\\subset Y$ such that for each neighborhood $O_{f(x)}\\subset Y$ of $f(x)$ there is a neighborhood $O_x\\subset X$ of $x$ such that $f(O_x)\\subset O_{f(x)}\\cup K_x$ and the set $K_x\\setminus O_{f(x)}$ is finite. This characterization is applied to give an alternative proof of a classic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2319","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"}