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We prove that a normal functor $F:Comp\\to Comp$ is skeletal (which means that $F$ preserves skeletal epimorphisms) if and only if for any open surjective open map $f:X\\to Y$ between zero-dimensional compacta with two-element non-degeneracy set $N^f=\\{x\\in X:|f^{-1}(f(x))|>1\\}$ the map $Ff:FX\\to FY$ is skeletal. This characterization implies that each open normal functor is skeletal. The converse is not true even for normal functors of finite deg"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1108.4197","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-08-21T18:28:04Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"011b3cbfdc3aa061cd59b18114f7efaa97a37b96a8ccc61cf094c8a863305c18","abstract_canon_sha256":"ecad54337ac85aa051be969def28e713f94b70454668d3b079881049d0972bbc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:14.455154Z","signature_b64":"Yf3ES4HCmCodHyZ0pQvsHpbcu63+xBhQOBNw1oFnGVE4kgHnJ9NoY0RYlGd3X0oPq11jd+TZ+71Vu09TfAgSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7092160aa3707ad36297bf5606a3891e6437140e825e8b00f52492b53c73cd4","last_reissued_at":"2026-05-18T03:38:14.454586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:14.454586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On functors preserving skeletal maps and skeletally generated compacta","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.GN","authors_text":"Andrzej Kucharski, Marta Martynenko, Taras Banakh","submitted_at":"2011-08-21T18:28:04Z","abstract_excerpt":"A map $f:X\\to Y$ between topological spaces is skeletal if the preimage $f^{-1}(A)$ of each nowhere dense subset $A\\subset Y$ is nowhere dense in $X$. We prove that a normal functor $F:Comp\\to Comp$ is skeletal (which means that $F$ preserves skeletal epimorphisms) if and only if for any open surjective open map $f:X\\to Y$ between zero-dimensional compacta with two-element non-degeneracy set $N^f=\\{x\\in X:|f^{-1}(f(x))|>1\\}$ the map $Ff:FX\\to FY$ is skeletal. This characterization implies that each open normal functor is skeletal. 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