Good pairs and neighborhood deformation retracts: 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 proved8Proved, and every prerequisite is fully proved too.

graph LR n0["Strong deformation retracts"]:::fully_proved n1["Good pairs and neighborhood deformation retracts"]:::fully_proved n2["Standard-simplex boundary and horn pairs are good"]:::fully_proved n3("Restricting the quotient to a good-pair neighborhood"):::fully_proved n4["Enlarging to the chosen neighborhood preserves relative homology"]:::fully_proved n5("Good-pair relative homology is reduced quotient homology"):::fully_proved n6["The good-pair quotient comparison is natural"]:::fully_proved n7("A nonempty coproduct of pointed good pairs is good"):::fully_proved n1 --> n7 n1 --> n2 n1 --> n3 n1 --> n4 n1 --> n5 n1 --> n6 n4 -.-> n5 n5 --> n6 n0 --> n7 n0 --> n1 click n0 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#strong-deformation-retract" "Strong deformation retracts — 1 item · 1 fully proved" class n1 focus 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" 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/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-neighborhood-quotient" "Restricting the quotient to a good-pair neighborhood — 1 item · 1 fully proved" click n4 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-neighborhood-relative-homology" "Enlarging to the chosen neighborhood preserves relative homology — 1 item · 1 fully proved" click n5 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-point-quotient-relative-homology" "Good-pair relative homology is reduced quotient homology — 1 item · 1 fully proved" click n6 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-quotient-comparison-naturality" "The good-pair quotient comparison is natural — 1 item · 1 fully proved" click n7 "../../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#sigma-good-pair" "A nonempty coproduct of pointed good pairs is good — 1 item · 1 fully proved"