Open domain refers to a point set that satisfies the following two conditions:

(1) is completely composed of interior points;

(2) Connectivity, that is, any two points in a point set can be connected by a broken line, and all points on the broken line are in this open domain.

Closed domain: open domain and its boundary.

Region: A set of points consisting of an open domain, a closed domain or a part of an open domain and its boundary points.

PS: Generally speaking, domain refers to open domain.

References:

Complex Function, edited by Shi Jihuai and Liu Taishun, University of Science and Technology of China Press, p. 1 edition, 29 pages.