In my version of Bott and Tu, the example reads (emphasis mine):
Moreover, if $V \subset U$ is an inclusion of CONTRACTIBLE open sets, then $\rho^U_V: H^q(\pi^{-1} U) \to H^q( \pi^{-1} V)$ is an isomorphism.
Greg Friedman
- 5.5k
- 23
- 38