Barycentric subdivision contracts simplex diameter: 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 proved3Proved, and every prerequisite is fully proved too.

graph LR n0("Affine barycentric subdivision is compatible with faces"):::fully_proved n1("Barycentric subdivision contracts simplex diameter"):::fully_proved n2("Iterated subdivision eventually makes every singular simplex small"):::fully_proved n0 --> n1 n1 -.-> n2 click n0 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#affine-barycentric-subdivision" "Affine barycentric subdivision is compatible with faces — 1 item · 1 fully proved" class n1 focus click n1 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#barycentric-subdivision-diameter" "Barycentric subdivision contracts simplex diameter — 1 item · 1 fully proved" click n2 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#eventually-small-singular-simplices" "Iterated subdivision eventually makes every singular simplex small — 1 item · 1 fully proved"