The path-class universal-cover 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. fully proved7Proved, and every prerequisite is fully proved too.
graph LR
n0["Semilocally simply-connected spaces"]:::fully_proved
n1["The path-class universal-cover space"]:::fully_proved
n2["The covering space associated to a subgroup"]:::fully_proved
n3("The sets U[γ] form the universal-cover basis"):::fully_proved
n4("The endpoint map is a covering"):::fully_proved
n5["The path-class cover is path-connected"]:::fully_proved
n6("The path-class cover is simply-connected"):::fully_proved
n0 --> n1
n3 -.-> n4
n3 -.-> n5
n4 -.-> n6
n5 -.-> n6
n1 --> n2
n1 --> n3
n1 --> n4
n1 --> n5
n1 --> n6
click n0 "../../../../../roadmap/fundamental-group/covering-spaces/universal-cover/index.html#semilocally-simply-connected" "Semilocally simply-connected spaces — 1 item · 1 fully proved"
class n1 focus
click n1 "../../../../../roadmap/fundamental-group/covering-spaces/universal-cover/index.html#universal-cover-path-space" "The path-class universal-cover space — 1 item · 1 fully proved"
click n2 "../../../../../roadmap/fundamental-group/covering-spaces/index.html#subgroup-cover-space" "The covering space associated to a subgroup — 1 item · 1 fully proved"
click n3 "../../../../../roadmap/fundamental-group/covering-spaces/universal-cover/index.html#universal-cover-basis" "The sets U[γ] form the universal-cover basis — 1 item · 1 fully proved"
click n4 "../../../../../roadmap/fundamental-group/covering-spaces/universal-cover/index.html#universal-cover-is-covering" "The endpoint map is a covering — 1 item · 1 fully proved"
click n5 "../../../../../roadmap/fundamental-group/covering-spaces/universal-cover/index.html#universal-cover-path-connected" "The path-class cover is path-connected — 1 item · 1 fully proved"
click n6 "../../../../../roadmap/fundamental-group/covering-spaces/universal-cover/index.html#universal-cover-simply-connected" "The path-class cover is simply-connected — 1 item · 1 fully proved"