# Def'n of holomorphically convex domain

1. Dec 4, 2008

### lark

Does anyone have a textbook on multivariable complex analysis, and do they define a holomorphically convex domain in terms of the union of an ascending series of compact subsets? If so, how exactly does the definition go?
Was it $$D=\bigcup K_n$$ where $$K_n$$ is holomorphically convex and compact and $$K_n \subset K_{n+1}?$$
Or $$D=\bigcup K_n$$ where $$K_n$$ is holomorphically convex and compact and $$K_n \subset \text{interior} (K_{n+1})?$$
Laura