In mathematical analysis, the word region usually refers to a subset of or that is open (in the standard Euclidean topology), simply connected and non-empty. A closed region is sometimes defined to be the closure of a region.
Regions and closed regions are often used as domains of functions or differential equations.
According to Kreyszig,
- A region is a set consisting of a domain plus, perhaps, some or all of its boundary points. (The reader is warned that some authors use the term "region" for what we call a domain [following standard terminology], and others make no distinction between the two terms.)
According to Yue Kuen Kwok,
- An open connected set is called an open region or domain. ...to an open region we may add none, some, or all its limit points, and simply call the new set a region.