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| In [[mathematical analysis]], the word '''''region''''' usually refers to a subset of <math>\R^n</math> or <math>\C^n</math> that is [[open set|open]] (in the standard [[Euclidean topology]]), [[connected set|connected]] and [[empty set|non-empty]]. A '''closed region''' is sometimes defined to be the [[closure (topology)|closure]] of a region.
| | My name is Alison and I am studying Dance and Hotel Administration at Torrig L / Denmark.<br><br>Here is my site - [http://goo.gl/a2UDem Cara membuat website] |
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| Regions and closed regions are often used as domains of functions or differential equations.
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| According to Kreyszig,<ref>[[Erwin Kreyszig]] (1993) ''Advanced Engineering Mathematics'', 7th edition, p. 720, [[John Wiley & Sons]], ISBN 0-471-55380-8</ref>
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| :A region is a set consisting of a [[domain (mathematical analysis)|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.)
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| According to Yue Kuen Kwok,
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| :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''.<ref>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</ref> | |
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| ==See also==
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| * [[Jordan curve theorem]]
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| * [[Riemann mapping theorem]]
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| * [[Domain (mathematical analysis)]]
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| ==Notes and references==
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| {{Reflist}}
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| * Ruel V. Churchill (1960) ''Complex variables and applications'', 2nd edition, §1.9 Regions in the complex plane, pp. 16 to 18, [[McGraw-Hill]]
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| * [[Constantin Carathéodory]] (1954) ''Theory of Functions of a Complex Variable'', v. I, p. 97, [[Chelsea Publishing]].
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| * [[Howard Eves]] (1966) ''Functions of a Complex Variable'', p. 105, Prindle, Weber & Schmidt.
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| [[Category:Mathematical analysis]]
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| [[Category:Topology]]
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My name is Alison and I am studying Dance and Hotel Administration at Torrig L / Denmark.
Here is my site - Cara membuat website