Borsuk–Ulam for the two-sphere: 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("The fundamental group of the circle"):::fully_proved n1("Higher spheres are simply connected"):::fully_proved n2("Borsuk–Ulam for the two-sphere"):::fully_proved n3("Three closed sets covering the sphere contain an antipodal pair"):::fully_proved n2 --> n3 n0 --> n2 n1 --> n2 click n0 "../../../../roadmap/fundamental-group/basic-constructions/index.html#fundamental-group-circle" "The fundamental group of the circle — 1 item · 1 fully proved" click n1 "../../../../roadmap/fundamental-group/basic-constructions/index.html#sphere-simply-connected" "Higher spheres are simply connected — 1 item · 1 fully proved" class n2 focus click n2 "../../../../roadmap/fundamental-group/basic-constructions/index.html#borsuk-ulam-sphere" "Borsuk–Ulam for the two-sphere — 1 item · 1 fully proved" click n3 "../../../../roadmap/fundamental-group/basic-constructions/index.html#three-closed-sets-antipodal" "Three closed sets covering the sphere contain an antipodal pair — 1 item · 1 fully proved"