Extendability Theorem for Intersection Numbers/Corollary

Corollary to Extendability Theorem for Intersection Numbers
Let $f: X \to Y$ be a smooth map of compact oriented manifolds having the same dimension.

Let $X = \partial W$, where $W$ is compact.

If there is a smooth map $g: W \to Y$ such that $g \restriction_X = f$, then:
 * $\deg \left({f}\right) = 0$

where $\deg \left({f}\right)$ denotes the degree of $f$.

Proof
Follows immediately from the Extendability Theorem for Intersection Numbers.