In mathematical analysis
, the word ''region'' usually refers to a subset
that is open
(in the standard Euclidean topology
), simply connected
. 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 point
s, 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, ]
* Interval (mathematics)
* Jordan curve theorem
* Locus (mathematics)
* Neighbourhood (mathematics)
* Point (geometry)
* Riemann mapping theorem
* 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.