{"paper":{"title":"On scatteredly continuous maps between topological spaces","license":"","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GT","authors_text":"B.Bokalo, T.Banakh","submitted_at":"2008-01-14T18:48:55Z","abstract_excerpt":"A map $f:X\\to Y$ between topological spaces is defined to be {\\em scatteredly continuous} if for each subspace $A\\subset X$ the restriction $f|A$ has a point of continuity. We show that for a function $f:X\\to Y$ from a perfectly paracompact hereditarily Baire Preiss-Simon space $X$ into a regular space $Y$ the scattered continuity of $f$ is equivalent to (i) the weak discontinuity (for each subset $A\\subset X$ the set $D(f|A)$ of discontinuity points of $f|A$ is nowhere dense in $A$), (ii) the $\\sigma$-continuity ($X$ can be written as a countable union of closed subsets on which $f$ is contin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.2131","kind":"arxiv","version":3},"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"}