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.)
^{[1]}

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*.^{[2]}

## See also

- Area
- Curve
- Interval (mathematics)
- Jordan curve theorem
- Locus (mathematics)
- Neighbourhood (mathematics)
- Point (geometry)
- Riemann mapping theorem
- Shape

## Notes

**^**Erwin Kreyszig (1993)*Advanced Engineering Mathematics*, 7th edition, p. 720, John Wiley & Sons, ISBN 0-471-55380-8**^**Yue Kuen Kwok (2002)*Applied Complex Variables for Scientists and Engineers*, § 1.4 Some topological definitions, p 23, Cambridge University Press, ISBN 0-521-00462-4

## References

- Ruel V. Churchill (1960)
*Complex variables and applications*, 2nd edition, §1.9 Regions in the complex plane, pp. 16 to 18, McGraw-Hill - Constantin Carathéodory (1954)
*Theory of Functions of a Complex Variable*, v. I, p. 97, Chelsea Publishing. - Howard Eves (1966)
*Functions of a Complex Variable*, p. 105, Prindle, Weber & Schmidt.