The auxiliary cover basepoint transports to the original basepoint: 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. fully proved7Proved, and every prerequisite is fully proved too.
graph LR
n0("Hatcher's binary cover of the strip enlargement"):::fully_proved
n1["The base-side auxiliary cover retracts onto the original space"]:::fully_proved
n2["The auxiliary cover basepoint transports to the original basepoint"]:::fully_proved
n3("An open-cover model for attached cells"):::fully_proved
n4["Attaching higher cells preserves the fundamental group"]:::fully_proved
n5("Overlap meridians recover the attaching loops"):::fully_proved
n6["Attaching 2-cells adds the attaching relations"]:::fully_proved
n3 -.-> n4
n3 --> n6
n1 -.-> n3
n1 --> n2
n0 -.-> n3
n0 --> n1
n0 --> n2
n2 -.-> n4
n2 --> n6
n2 -.-> n3
n2 --> n5
n5 --> n6
click n0 "../../../../../../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 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"
class n2 focus
click n2 "../../../../../../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 n3 "../../../../../../roadmap/fundamental-group/van-kampen/index.html#cell-attachment-cover-model" "An open-cover model for attached cells — 1 item · 1 fully proved"
click n4 "../../../../../../roadmap/fundamental-group/van-kampen/index.html#attach-higher-cells-fundamental-group" "Attaching higher cells preserves the fundamental group — 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/index.html#attach-two-cells-fundamental-group" "Attaching 2-cells adds the attaching relations — 1 item · 1 fully proved"