The path-class cover is path-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

fully proved5Proved, and every prerequisite is fully proved too.

graph LR n0["The path-class universal-cover space"]:::fully_proved n1("The sets U[γ] form the universal-cover basis"):::fully_proved n2["The path-class cover is path-connected"]:::fully_proved n3("The subgroup projection is a path-connected covering"):::fully_proved n4("The path-class cover is simply-connected"):::fully_proved n1 -.-> n3 n1 -.-> n2 n2 -.-> n3 n2 -.-> n4 n0 --> n1 n0 --> n2 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#universal-cover-basis" "The sets U[γ] form the universal-cover basis — 1 item · 1 fully proved" class n2 focus click n2 "../../../../../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 n3 "../../../../../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 n4 "../../../../../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"