Analytic polyhedron
In mathematics, especially several complex variables, an analytic polyhedron is a subset of the complex space Cn of the form P = { z ∈ D : | f j ( z ) | < 1 , 1 ≤ j ≤ N } {\displaystyle P=\{z\in D:|f_{j}(z)|<1,\;\;1\leq j\leq N\}} where D is a bounded connected open subset of Cn, f j {\displaystyle f_{j}} are holomorphic on D and P is assumed to be relatively compact in D. If f j {\displaystyle f_{j}} above are polynomials, then the set is called a polynomial polyhedron. Every analytic polyhedron is a domain of holomorphy and it is thus pseudo-convex.