Domain (mathematical analysis)

In the Topology and Analysis, the term territory refers to an open, non-empty and connected subset of a topological space. In many sets of function theory it is assumed that the considered functions defined in an area and are holomorphic or meromorphic.

Remarks and examples

• Is called star-shaped domain, if D is star-shaped and one territory.
• Is called convex domain, if D is convex and an area is.
• Each convex area is a star-shaped domain.