Subcomplex decompositions admit compatible neighborhoods: 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["Intersections of CW subcomplexes"]:::fully_proved n1["A common regular-neighborhood system for subcomplexes"]:::fully_proved n2["A regular neighborhood strongly deformation retracts onto its subcomplex"]:::fully_proved n3("Subcomplex decompositions admit compatible neighborhoods"):::fully_proved n4("Excision holds for a union of CW subcomplexes"):::fully_proved n2 --> n3 n1 --> n2 n1 --> n3 n0 --> n1 n0 --> n3 n3 -.-> n4 click n0 "../../../../../../roadmap/homology/computations-and-applications/post-excision-applications/cw-subcomplex-neighborhood/index.html#subcomplex-intersection" "Intersections of CW subcomplexes — 1 item · 1 fully proved" click n1 "../../../../../../roadmap/homology/computations-and-applications/post-excision-applications/cw-subcomplex-neighborhood/index.html#regular-neighborhood-system" "A common regular-neighborhood system for subcomplexes — 1 item · 1 fully proved" click n2 "../../../../../../roadmap/homology/computations-and-applications/post-excision-applications/cw-subcomplex-neighborhood/index.html#regular-neighborhood-strong-deformation-retract" "A regular neighborhood strongly deformation retracts onto its subcomplex — 1 item · 1 fully proved" class n3 focus click n3 "../../../../../../roadmap/homology/computations-and-applications/post-excision-applications/cw-subcomplex-neighborhood/index.html#subcomplex-neighborhood-cover" "Subcomplex decompositions admit compatible neighborhoods — 1 item · 1 fully proved" click n4 "../../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#cw-subcomplex-excision" "Excision holds for a union of CW subcomplexes — 1 item · 1 fully proved"