A common regular-neighborhood system for subcomplexes: 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["The radial collar of a cell boundary"]:::fully_proved n2["A common regular-neighborhood system for subcomplexes"]:::fully_proved n3["A regular neighborhood strongly deformation retracts onto its subcomplex"]:::fully_proved n4("Subcomplex decompositions admit compatible neighborhoods"):::fully_proved n1 --> n2 n3 --> n4 n2 --> n3 n2 --> n4 n0 --> n2 n0 --> 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#cell-boundary-collar" "The radial collar of a cell boundary — 1 item · 1 fully proved" class n2 focus click n2 "../../../../../../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 n3 "../../../../../../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" click n4 "../../../../../../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"