A nonsurjective sphere map has degree zero: 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("Degree is the multiplier of the ordered sphere class"):::fully_proved n2["A punctured sphere is Euclidean space"]:::fully_proved n3("A nonsurjective sphere map has degree zero"):::fully_proved n2 -.-> n3 n1 --> n3 n0 -.-> n3 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/degree/index.html#sphere-degree-definition" "Degree is the multiplier of the ordered sphere class — 1 item · 1 fully proved" click n2 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#punctured-sphere-stereographic" "A punctured sphere is Euclidean space — 1 item · 1 fully proved" class n3 focus click n3 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#nonsurjective-degree-zero" "A nonsurjective sphere map has degree zero — 1 item · 1 fully proved"