real analytic subvariety
Let be an open set.
If is not required to be closed, then it is said to be a local real analytic subvariety. Sometimes is called a real analytic set or real analytic variety. Similarly as for complex analytic sets we can also define the regular and singular points.
The set of regular points of is denoted by or sometimes The set of singular points is no longer a subvariety as in the complex case, though it can be sown to be semianalytic. In general, real subvarieties is far worse behaved than their complex counterparts.
- 1 Jacek Bochnak, Michel Coste, Marie-Francoise Roy. . Springer, 1998.
|Title||real analytic subvariety|
|Date of creation||2013-03-22 17:41:07|
|Last modified on||2013-03-22 17:41:07|
|Last modified by||jirka (4157)|
|Synonym||real analytic variety|
|Synonym||real analytic set|
|Defines||real algebraic variety|
|Defines||real algebraic subvariety|
|Defines||local real analytic subvariety|