Zeroth homology is free on path components: local context

Project map · Chapter map · Full theorem DAG · Open textbook statement

This local map shows one dependency hop in either direction. The highlighted item is the current focus. What the colours mean

in mathlib2Upstreamed into Mathlib.fully proved2Proved, and every prerequisite is fully proved too.

graph LR n0["Singular homology"]:::mathlib n1["Zeroth homology is free on path components"]:::mathlib n2("Homology of a point"):::fully_proved n3("Reduced homology of the zero-sphere"):::fully_proved n0 --> n2 n0 --> n1 n1 -.-> n3 n1 -.-> n2 click n0 "../../../../roadmap/homology/simplicial-and-singular/index.html#singular-homology" "Singular homology — 1 item · 1 in mathlib" class n1 focus click n1 "../../../../roadmap/homology/simplicial-and-singular/index.html#zeroth-homology-components" "Zeroth homology is free on path components — 1 item · 1 in mathlib" click n2 "../../../../roadmap/homology/simplicial-and-singular/index.html#point-homology" "Homology of a point — 1 item · 1 fully proved" click n3 "../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#zero-sphere-reduced-homology" "Reduced homology of the zero-sphere — 1 item · 1 fully proved"