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We prove that every equicontinuous factor of the flow $(K, G)$ is isomorphic to a flow on a compact abelian Lie group of dimension less than $b_1(K)$. For this purpose, we use and provide a new proof for [HJop, Theorem 2.12] which states that for a flow on a locally connected compact space the quotient map onto the maximal equicontinuous factor is monotone, i.e., has connected "},"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":"1904.12203","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-27T20:22:03Z","cross_cats_sorted":[],"title_canon_sha256":"edb113933bce411ad5d7c6824580b66f6d10ead2ee5c375cd1cde8b7fc6a0947","abstract_canon_sha256":"7437fb965560eab585d14dca3b7cefb238cf28daa5e968369cbfb89676053697"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:38.691859Z","signature_b64":"GV40SmvMqnwhB6ZbJL5LOq44YGNblQvvqu6bxSl0Eh88+vYCOS9dBkoqgxOKKBcYGX/FOPjS9OaNhz/snNmxAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eeaba903fe8fbe2e64817816afa0d103d36f3ae46f024c68bb5498637dba1549","last_reissued_at":"2026-05-17T23:47:38.691298Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:38.691298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On equicontinuous factors of flows on locally path-connected compact spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Nikolai Edeko","submitted_at":"2019-04-27T20:22:03Z","abstract_excerpt":"We consider a locally path-connected compact metric space $K$ with finite first Betti number $b_1(K)$ and a flow $(K, G)$ on $K$ such that $G$ is abelian and all $G$-invariant functions $f\\in\\mathrm{C}(K)$ are constant. We prove that every equicontinuous factor of the flow $(K, G)$ is isomorphic to a flow on a compact abelian Lie group of dimension less than $b_1(K)$. 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