The 2-skeleton of a path-connected CW complex 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("Compact subsets lie in a bounded skeleton"):::fully_proved n1["Classical skeleton inclusions are abstract cell attachments"]:::fully_proved n2("Higher-cell attachments preserve path components"):::fully_proved n3("The 2-skeleton of a path-connected CW complex is path-connected"):::fully_proved n4["Finite skeleta above dimension two have the same fundamental group"]:::fully_proved n0 -.-> n3 n1 -.-> n3 n1 -.-> n4 n2 -.-> n3 n2 -.-> n4 n3 -.-> n4 click n0 "../../../../../roadmap/appendix/classical-cw-bridge/index.html#compact-subset-bounded-skeleton" "Compact subsets lie in a bounded skeleton — 1 item · 1 fully proved" click n1 "../../../../../roadmap/appendix/index.html#classical-skeleton-cell-attachment" "Classical skeleton inclusions are abstract cell attachments — 1 item · 1 fully proved" click n2 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#higher-cell-attachment-path-components" "Higher-cell attachments preserve path components — 1 item · 1 fully proved" class n3 focus click n3 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#path-connected-two-skeleton" "The 2-skeleton of a path-connected CW complex is path-connected — 1 item · 1 fully proved" click n4 "../../../../../roadmap/fundamental-group/van-kampen/index.html#finite-skeleton-fundamental-group" "Finite skeleta above dimension two have the same fundamental group — 1 item · 1 fully proved"