Let r be a region. If all the interiors of any simple closed curve in R belong to R, then R is called a simply connected region. More generally, a single connected region is a region without "holes" and a multi-connected region is a region with "holes".

Green's formula:

Green's formula is a mathematical formula, which describes the close relationship between the curve integral of coordinates along the closed curve L on the plane and the double integral on the closed area D surrounded by the curve L, and is generally used for the total differential quadrature of binary functions.

Let D be a plane region. If some regions surrounded by any closed curve in D belong to D, D is called a plane simply connected region. Intuitively speaking, a simply connected region is a region without space, otherwise it is called a complex connected region.

A curve is called a closed curve when its starting point and ending point coincide on the xOy plane. Let the plane closed curve L surround the plane area D, and stipulate that when a person turns around along the closed curve L, the area D is always on the left side of the person, that is to say, the walking direction of the person is the positive direction of the curve L relative to the area D, and vice versa.

Refer to the above? Baidu Encyclopedia-Green Formula