The covering space associated to a subgroup: 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 proved5Proved, and every prerequisite is fully proved too.

graph LR n0["The path-class universal-cover space"]:::fully_proved n1["The covering space associated to a subgroup"]:::fully_proved n2("The subgroup projection is a path-connected covering"):::fully_proved n3("The subgroup cover realizes the chosen subgroup"):::fully_proved n4["Pointed connected covers are classified by subgroups"]:::fully_proved n3 -.-> n4 n2 -.-> n3 n1 -.-> n4 n1 --> n3 n1 --> n2 n0 --> n1 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" class n1 focus click n1 "../../../../roadmap/fundamental-group/covering-spaces/index.html#subgroup-cover-space" "The covering space associated to a subgroup — 1 item · 1 fully proved" click n2 "../../../../roadmap/fundamental-group/covering-spaces/index.html#subgroup-cover-is-covering" "The subgroup projection is a path-connected covering — 1 item · 1 fully proved" click n3 "../../../../roadmap/fundamental-group/covering-spaces/index.html#subgroup-cover-image" "The subgroup cover realizes the chosen subgroup — 1 item · 1 fully proved" click n4 "../../../../roadmap/fundamental-group/covering-spaces/index.html#pointed-cover-classification" "Pointed connected covers are classified by subgroups — 1 item · 1 fully proved"