Relative homology in a contractible ambient space: 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("The reduced long exact sequence of a nonempty pair"):::fully_proved n1("Reduced homology of a contractible space vanishes"):::fully_proved n2["Relative homology in a contractible ambient space"]:::fully_proved n3("Local homology of positive-dimensional Euclidean space"):::fully_proved n2 -.-> n3 n1 -.-> n2 n0 --> n2 click n0 "../../../../../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 n1 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#contractible-space-reduced-homology" "Reduced homology of a contractible space vanishes — 1 item · 1 fully proved" class n2 focus click n2 "../../../../../roadmap/homology/computations-and-applications/local-homology-and-dimension/index.html#contractible-ambient-relative-homology" "Relative homology in a contractible ambient space — 1 item · 1 fully proved" click n3 "../../../../../roadmap/homology/computations-and-applications/local-homology-and-dimension/index.html#punctured-euclidean-local-homology" "Local homology of positive-dimensional Euclidean space — 1 item · 1 fully proved"