If the nullspace of a transformation is trivial, then is a basis for the nullspace the emptyset?
I suppose it is a matter of convention.
I prefer the convention that the trivial vector space has the emptyset as basis, partly because then we have no exceptions to the statement "all vector spaces have a basis", and partly because the number of elements in the emptyset is 0, coinciding with the usual idea that the dimension of a point is 0 (and thus being consistent with the dimension of vector spaces being equal to the number of elements in a basis).