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

## References

• 1 Hassler Whitney. . Addison-Wesley, Philippines, 1972.
Title intersection of complex analytic varieties is a complex analytic variety IntersectionOfComplexAnalyticVarietiesIsAComplexAnalyticVariety 2013-03-22 14:59:31 2013-03-22 14:59:31 jirka (4157) jirka (4157) 6 jirka (4157) Theorem msc 32A60