In mathematical analysis, the word ''region'' usually refers to a subset of $\backslash R^n$ or $\backslash Complex^n$ 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 ollowing 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''.Yue Kuen Kwok (2002) ''Applied Complex Variables for Scientists and Engineers'', § 1.4 Some topological definitions, p 23, Cambridge University Press,

** See also **

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

** Notes **

{{Reflist

** 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.
Category:Mathematical analysis
Category:Topology