In mathematical analysis, a domain or region is a non-empty, connected, and open set in a topological space.
[a] The basic idea of a connected subset of a space dates from the 19th century, but precise definitions vary slightly from generation to generation, author to author, and edition to edition, as concepts developed and terms were translated between German, French, and English works.
In the study of several complex variables, the definition of a domain is extended to include any connected open subset of Cn.
In Euclidean spaces, one-, two-, and three-dimensional regions are curves, surfaces, and solids, whose extent are called, respectively, length, area, and volume.
German: Eine offene Punktmenge heißt zusammenhängend, wenn man sie nicht als Summe von zwei offenen Punktmengen darstellen kann.