The subgroup cover realizes the chosen 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 induced subgroup consists of loops with closed lifts"):::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 n0 -.-> n3 n3 -.-> n4 n2 -.-> n3 n1 -.-> n4 n1 --> n3 n1 --> n2 click n0 "../../../../roadmap/fundamental-group/covering-spaces/index.html#closed-lift-image" "The induced subgroup consists of loops with closed lifts — 1 item · 1 fully proved" 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" class n3 focus 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"