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To prove this result we show a generalization of a theorem of Burgess about Borel selectors for the orbit equivalence relation induced by a group action and also show that some properties of the Vaught's transform are valid for partial actions of groups."},"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":"1702.02611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-02-08T21:15:15Z","cross_cats_sorted":["math.GN","math.OA"],"title_canon_sha256":"5052ed86d3354ec97df61c0bdff65af8d6b8e08cc13108e23d419961baaac665","abstract_canon_sha256":"85b4f5324405d579836cc88a4ec1a169f8ff07aa407b5d13842a95b829a67d7c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:03.865789Z","signature_b64":"lM+mn66RMUmMeXNFjNSVNeRbiJ1eSiigWFHlvpSr2uN5KAwa2/xsxp0aK8cM35zr7U8H5vWbuKcS71kHKwjZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9090549dea22a077a7ea2d5b4a59dc21ea0cf65c9f5fe87adad38f721d19f07c","last_reissued_at":"2026-05-18T00:51:03.865357Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:03.865357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Borel Globalizations of Partial Actions of Polish Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.OA"],"primary_cat":"math.LO","authors_text":"Carlos Uzcategui, Hector Pinedo","submitted_at":"2017-02-08T21:15:15Z","abstract_excerpt":"We show that the enveloping space $X_G$ of a partial action of a Polish group $G$ on a Polish space $X$ is a standard Borel space, that is to say, there is a topology $\\tau$ on $X_G$ such that $(X_G, \\tau)$ is Polish and the quotient Borel structure on $X_G$ is equal to $Borel(X_G,\\tau)$. 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