The path-class cover is simply-connected: 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

in mathlib1Upstreamed into Mathlib.fully proved5Proved, and every prerequisite is fully proved too.

graph LR n0("The induced subgroup consists of loops with closed lifts"):::fully_proved n1("Covering maps inject path-homotopy classes"):::mathlib n2["The path-class universal-cover space"]:::fully_proved n3("The endpoint map is a covering"):::fully_proved n4["The path-class cover is path-connected"]:::fully_proved n5("The path-class cover is simply-connected"):::fully_proved n0 -.-> n5 n1 -.-> n5 n3 -.-> n5 n4 -.-> n5 n2 --> n3 n2 --> n4 n2 --> n5 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#covering-injective-path-classes" "Covering maps inject path-homotopy classes — 1 item · 1 in mathlib" click n2 "../../../../../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 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" class n5 focus click n5 "../../../../../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"