Standard-simplex boundary and horn pairs are good: 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 boundary and zero horn of a standard topological simplex"]:::fully_proved n1["Good pairs and neighborhood deformation retracts"]:::fully_proved n2["Standard-simplex boundary and horn pairs are good"]:::fully_proved n3("The zero face induces an isomorphism in relative homology"):::fully_proved n4("The first simplex computes homology relative to the second"):::fully_proved n2 -.-> n4 n2 -.-> n3 n0 --> n2 n0 --> n3 n3 -.-> n4 n1 --> n2 click n0 "../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#standard-simplex-boundary-horn" "The boundary and zero horn of a standard topological simplex — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-data" "Good pairs and neighborhood deformation retracts — 1 item · 1 fully proved" class n2 focus click n2 "../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#standard-simplex-boundary-good-pairs" "Standard-simplex boundary and horn pairs are good — 1 item · 1 fully proved" click n3 "../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#standard-simplex-zero-face-relative-homology" "The zero face induces an isomorphism in relative homology — 1 item · 1 fully proved" click n4 "../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#double-simplex-relative-comparison" "The first simplex computes homology relative to the second — 1 item · 1 fully proved"