The base-side cone cover retracts onto the original 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("A single cone attachment has a two-set open cover"):::fully_proved n1["The base-side cone cover retracts onto the original space"]:::fully_proved n2["The base-side auxiliary cover retracts onto the original space"]:::fully_proved n3["The mapping-cone cover has the relative homology of the original pair"]:::fully_proved n1 -.-> n2 n1 -.-> n3 n0 --> n1 click n0 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#single-cone-open-cover" "A single cone attachment has a two-set open cover — 1 item · 1 fully proved" class n1 focus click n1 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#single-cone-base-retract" "The base-side cone cover retracts onto the original space — 1 item · 1 fully proved" click n2 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-base-cover-retract" "The base-side auxiliary cover retracts onto the original space — 1 item · 1 fully proved" click n3 "../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#mapping-cone-cover-relative-homology" "The mapping-cone cover has the relative homology of the original pair — 1 item · 1 fully proved"