Actually, the proof gives an even more precise conclusion: ......
Nevertheless, it might be possible to make sense of (2) even for non-injective $V$ by considering a multi-valued operator $Z$.
This is true even if $H^{2}(B)=0$, as evidenced by the existence of manifolds whose affine base is a Klein bottle.
Even though we were able to derive a formula for ......, it is not easy to use.
The fact that the number $T(p)$ is uniquely defined, even though $p$ is not, enables us to define the nullity of $A$ as follows.
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