intersection of complex analytic varieties is a complex analytic variety

A useful result allowing us to define the “smallest” analytic variety is the following.

Theorem.

Let $G\mathrm{\subset }{\mathrm{C}}^N$ be an open set, then an arbitrary intersection of complex analytic varieties in $G$ is a complex analytic variety in $G$.

Title	intersection of complex analytic varieties is a complex analytic variety
Canonical name	IntersectionOfComplexAnalyticVarietiesIsAComplexAnalyticVariety
Date of creation	2013-03-22 14:59:31
Last modified on	2013-03-22 14:59:31
Owner	jirka (4157)
Last modified by	jirka (4157)
Numerical id	6
Author	jirka (4157)
Entry type	Theorem
Classification	msc 32A60