Small augmented chains include by a chain-homotopy equivalence: 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 proved5Proved, and every prerequisite is fully proved too.

graph LR n0["The augmented singular chain complex"]:::fully_proved n1["Small singular chains include by a chain-homotopy equivalence"]:::fully_proved n2["Small augmented chains include by a chain-homotopy equivalence"]:::fully_proved n3("Augmented binary-cover chains form a short exact sequence"):::fully_proved n4("The reduced binary-cover Mayer–Vietoris sequence"):::fully_proved n3 --> n4 n2 --> n3 n2 -.-> n4 n0 --> n3 n0 --> n2 n1 --> n2 click n0 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#augmented-singular-chain-complex" "The augmented singular chain complex — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#small-chain-inclusion-homotopy-equivalence" "Small singular chains include by a chain-homotopy equivalence — 1 item · 1 fully proved" class n2 focus click n2 "../../../../../roadmap/homology/computations-and-applications/mayer-vietoris/index.html#small-augmented-chain-inclusion-homotopy-equivalence" "Small augmented chains include by a chain-homotopy equivalence — 1 item · 1 fully proved" click n3 "../../../../../roadmap/homology/computations-and-applications/mayer-vietoris/index.html#augmented-binary-cover-chain-short-exact-sequence" "Augmented binary-cover chains form a short exact sequence — 1 item · 1 fully proved" click n4 "../../../../../roadmap/homology/computations-and-applications/mayer-vietoris/index.html#reduced-binary-cover-mayer-vietoris-sequence" "The reduced binary-cover Mayer–Vietoris sequence — 1 item · 1 fully proved"