  We give a simple and more elementary proof that the notions of Domain of
Holomorphy and Weak Domain of Holomorphy are equivalent. This proof is based on
a combination of Baire's Category Theorem and Montel's Theorem. We also obtain
generalizations by demanding that the non-extentable functions belong to a
particular class of holomorphic functions in the domain. We give an example of
a domain in the plane which is a domain of holomorphy with respect to the class
of all holomorphic functions but not with respect to the class of holomorphic
functions continuously extendable on the closure of the domain.
