Abstract
Let D be an arbitrary domain in C-n, n > 1, and M subset of partial derivative D be an open piece of the boundary. Suppose that M is connected and partial derivative D is smooth real-analytic of finite type (in the sense of D'Angelo) in a neighborhood of (M) over bar. Let f : D -> C-n be a holomorphic correspondence such that the cluster set d(f)(M) is contained in a smooth closed real-algebraic hypersurface M' in C-n of finite type. It is shown that if f extends continuously to some open peace of M, then f extends as a holomorphic correspondence across M. As an application, we prove that any proper holomorphic correspondence from a bounded domain D in C-n with smooth real-analytic boundary onto a bounded domain D' in C-n. with smooth real-algebraic boundary extends as a holomorphic correspondence to a neighborhood of (D) over bar.