Remmert–Stein Theorem

(Theorems In Complex Analysis)


Theorems In Complex Analysis since 1953
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What is Remmert–Stein theorem?

In complex analysis, a field in mathematics, the Remmert–Stein theorem, introduced by Reinhold Remmert and Karl Stein , gives conditions for the closure of an analytic set to be analytic. The theorem states that if F is an analytic set of dimension less than k in some complex manifold D, and M is an analytic subset of D – F with all components of dimension at least k, then the closure of M is either analytic or contains F. The condition on the dimensions is necessary: for example, the set of points 1/n in the complex plane is analytic in the complex plane minus the origin, but its closure in the complex plane is not.

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Remmert-Stein theorem


Remmert–Steins sats (sv)

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