ABSTRACT
One of the basic results in the theory of holomorphic functions of one variable is Riemann’s theorem on removable singularities: any function that is holomorphic and uniformly bounded on the complement of a discrete set of points in an open subset D ⊆ ℂ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203750063/1087b710-7222-48dd-8094-26eaf896ae1b/content/eq455.tif"/> has a unique extension to a holomorphic function in all of D. The generalizations of this result to holomorphic functions of several variables exhibit interesting differences between function theory in one and in several variables.
