Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 114 / 4 / b / Solution

The small simplex theorem says that the inclusion of the subcomplex generated by singular simplices whose images lie wholly in $U$ or wholly in $V$,is a chain-homotopy equivalence. Repeated barycentric subdivision supplies the inverse up to chain homotopy.

Solved by gpt-5.6-sol high.