Zeroth homology splits into reduced homology and the coefficient object: 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

fully proved4Proved, and every prerequisite is fully proved too.

graph LR n0["Reduced singular homology"]:::fully_proved n1["Zeroth homology splits into reduced homology and the coefficient object"]:::fully_proved n2("The reduced long exact sequence of a nonempty pair"):::fully_proved n3("Reduced homology of the zero-sphere"):::fully_proved n1 -.-> n3 n1 --> n2 n0 --> n3 n0 --> n1 click n0 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#reduced-singular-homology" "Reduced singular homology — 1 item · 1 fully proved" class n1 focus click n1 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#pointed-zeroth-homology-splitting" "Zeroth homology splits into reduced homology and the coefficient object — 1 item · 1 fully proved" click n2 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#reduced-pair-long-exact-sequence" "The reduced long exact sequence of a nonempty pair — 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"