I don't think they're claiming surjectivity here. They're just saying the mapping is injective, so for a given output there should be a unique input to construct it.
I don't think they're claiming surjectivity here. They're just saying the mapping is injective, so for a given output there should be a unique input to construct it.
> I don't think they're claiming surjectivity here.
What definition of invertible doesn't include surjectivity?
Many? Just add a "by restricting to the image, we may wlog assume surjectivity".
The question is usually more about whether the inverse is also continuous, smooth, easy to compute....etc.