The sets U[γ] form the universal-cover basis: 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 proved6Proved, and every prerequisite is fully proved too.
graph LR
n0["The path-class universal-cover space"]:::fully_proved
n1("Small nullhomotopy neighborhoods form a basis"):::fully_proved
n2("The sets U[γ] form the universal-cover basis"):::fully_proved
n3("The endpoint map is a covering"):::fully_proved
n4["The path-class cover is path-connected"]:::fully_proved
n5("The subgroup projection is a path-connected covering"):::fully_proved
n1 -.-> n2
n2 -.-> n5
n2 -.-> n3
n2 -.-> n4
n3 -.-> n5
n4 -.-> n5
n0 --> n2
n0 --> n3
n0 --> n4
click n0 "../../../../../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 n1 "../../../../../roadmap/fundamental-group/covering-spaces/universal-cover/index.html#nullhomotopic-open-basis" "Small nullhomotopy neighborhoods form a basis — 1 item · 1 fully proved"
class n2 focus
click n2 "../../../../../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 n3 "../../../../../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 n4 "../../../../../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 n5 "../../../../../roadmap/fundamental-group/covering-spaces/index.html#subgroup-cover-is-covering" "The subgroup projection is a path-connected covering — 1 item · 1 fully proved"