ABSTRACT
One of the most interesting and characteristic phenomena observed in the study of holomorphic functions of several variables is the existence of pairs of open sets D ⊂ E ⊆ ℂ n such that every function that is holomorphic in D necessarily extends to a function that is holomorphic in the strictly larger set E; several examples of this have already been pointed out. It is clearly of some interest to determine those sets D for which no such extension is possible. As will later become apparent, such sets play a basic role in the function theory of several variables.
