I was flipping through Milnor's "Topology from the Differentiable Viewpoint," and I came upon a sentence concerning the mod 2 degree of a function from M to N. It essentially says: "We may as well assume also that N is compact without boundary, for otherwise the deg mod 2 would necessarily be zero."
I understand why this is true for compactness. However, any ideas I have trying to prove the boundary part seem way to complex for a paranthetical aside. Any ideas are appreciated.
Edit: Also, M and N are smooth manifolds of the same dimension, f is smooth, and M is assumed to be compact and boundaryless (so the definition of mod 2 degree makes sense).