Hatcher's auxiliary cell-attachment cover dependency map
This map shows the container's direct articles. Nested containers are collapsed and clickable; dependency edges are rolled up from their leaves. fully proved20Proved, and every prerequisite is fully proved too.
graph LR
n0["The strip enlargement retracts onto the attached space"]:::fully_proved
n1["The base-side auxiliary cover retracts onto the original space"]:::fully_proved
n2("Hatcher's binary cover of the strip enlargement"):::fully_proved
n3["The strip-enlarged cell-attachment space"]:::fully_proved
n4["The auxiliary cover basepoint transports to the original basepoint"]:::fully_proved
n5("Overlap meridians recover the attaching loops"):::fully_proved
n6("The auxiliary overlap has an indexed open cover"):::fully_proved
n7["Each overlap piece has the homotopy type of its attaching sphere"]:::fully_proved
n8("The strip-connected upper cover is contractible"):::fully_proved
n9["External chapter: The fundamental group<br/><small>11 items · 11 fully proved</small>"]:::boundary
n9 -.-> n1
n9 --> n3
n9 -->|2| n5
n9 -.-> n5
n9 -.-> n7
n9 -.-> n8
n0 -.-> n9
n1 -. 2 .-> n9
n1 --> n4
n2 -.-> n9
n2 --> n1
n2 --> n4
n2 --> n6
n2 --> n8
n3 --> n9
n3 --> n0
n3 --> n2
n4 --> n9
n4 -. 2 .-> n9
n4 --> n5
n5 --> n9
n6 -.-> n9
n6 --> n7
n7 -.-> n9
n7 --> n5
n8 -.-> n9
click n0 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-attachment-retract" "The strip enlargement retracts onto the attached space — 1 item · 1 fully proved"
click n1 "../../../../../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 n2 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-cell-attachment-open-cover" "Hatcher's binary cover of the strip enlargement — 1 item · 1 fully proved"
click n3 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-cell-attachment-space" "The strip-enlarged cell-attachment space — 1 item · 1 fully proved"
click n4 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-cover-basepoint-transport" "The auxiliary cover basepoint transports to the original basepoint — 1 item · 1 fully proved"
click n5 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-overlap-attaching-map" "Overlap meridians recover the attaching loops — 1 item · 1 fully proved"
click n6 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-overlap-open-cover" "The auxiliary overlap has an indexed open cover — 1 item · 1 fully proved"
click n7 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-overlap-piece-sphere" "Each overlap piece has the homotopy type of its attaching sphere — 1 item · 1 fully proved"
click n8 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-upper-cover-contractible" "The strip-connected upper cover is contractible — 1 item · 1 fully proved"
click n9 "../../../../chapters/fundamental-group.html" "The fundamental group — 11 items · 11 fully proved"