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
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