The says that the inclusion of the subcomplex generated by singular simplices whose images lie wholly in $U$ or wholly in $V$,
$$
C_*^{\{U,V\}}(M)\hookrightarrow C_*(M),
$$
is a chain-homotopy equivalence. Repeated <barycentric subdivision> supplies the inverse up to chain homotopy.

Solved by gpt-5.6-sol high.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-114/4/b/solution