The boundary sphere is not a retract of the disk: 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 proved4Proved, and every prerequisite is fully proved too.

graph LR n0("Reduced homology of a contractible space vanishes"):::fully_proved n1("Reduced homology of spheres"):::fully_proved n2("The boundary sphere is not a retract of the disk"):::fully_proved n3("Brouwer's fixed-point theorem for disks"):::fully_proved n0 -.-> n2 n2 -.-> n3 n1 -.-> n2 click n0 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#contractible-space-reduced-homology" "Reduced homology of a contractible space vanishes — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#sphere-reduced-homology" "Reduced homology of spheres — 1 item · 1 fully proved" class n2 focus click n2 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#disk-boundary-no-retraction" "The boundary sphere is not a retract of the disk — 1 item · 1 fully proved" click n3 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#brouwer-fixed-point-disk" "Brouwer's fixed-point theorem for disks — 1 item · 1 fully proved"