List of Suite PreCure episodes: Difference between revisions

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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.
 
Regions and closed regions are often used as domains of functions or differential equations.
 
According to Kreyszig,<ref>[[Erwin Kreyszig]] (1993) ''Advanced Engineering Mathematics'', 7th edition, p. 720, [[John Wiley & Sons]], ISBN 0-471-55380-8</ref>
: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.)
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''.<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>
 
==See also==
* [[Jordan curve theorem]]
* [[Riemann mapping theorem]]
* [[Domain (mathematical analysis)]]
 
==Notes and references==
{{Reflist}}
 
* 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]]

Revision as of 06:13, 6 January 2014

In mathematical analysis, the word region usually refers to a subset of ℝn or ℂn that is open (in the standard Euclidean topology), 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,[1]

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 [following 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.[2]

See also

Notes and references

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

  • 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.
  1. ↑ Erwin Kreyszig (1993) Advanced Engineering Mathematics, 7th edition, p. 720, John Wiley & Sons, ISBN 0-471-55380-8
  2. ↑ 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
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