Definition
A complex manifold of complex dimension is called a Stein manifold if the following conditions hold:
- is holomorphically convex, i.e. for every compact subset, the so-called holomorphic convex hull,
- is again a compact subset of . Here denotes the ring of holomorphic functions on .
- is holomorphically separable, i.e. if are two points in, then there is a holomorphic function
- such that
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