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In mathematical analysis, the word ''region'' usually refers to a subset of \R^n or \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


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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