Corollary: No separated witness in this module

If a closed $C\subseteq U\setminus U^{\circ }$ contains $Z\times \{0\}$, then for every extension $T$ and every $a\in H$ there is no open $G\subset U\setminus C$ with ${F_0}^T(a){|}_G\ne 0$. The contact-support obstruction test of XV-B therefore cannot produce an obstruction for any extension lift of this module.

Proof. Theorem thm:defect(ii).