Typically without is used to mean not having something.
He went to work without his pants on.
However, I'm wondering if it can be used for outside the bounds of.
We do this with within. For example:
Please keep your children within the bounds of the school.
So could the following:
The vigilante was operating without the bounds of the law (or)
The shop refused to refund my item, as it was without the warranty period.
be viewed as being acceptable?