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Mar 22, 2011 at 7:30 comment added Stefan Waldmann @Vamsi: OK, I understand. But for the above statement the manifold itself is connected, only the charts may be very non-connected countably many components if your manifold is second countable ;) Another thing: maybe you should look at the theory of Stein manifolds, they have a rich structure theory and canbe embedded into $\mathbb{C}^n$.
Mar 21, 2011 at 20:02 comment added Vamsi Actually I don't want them to have infinitely many connected components. I want finitely many components. Thanks for the reference anyway.
Mar 21, 2011 at 8:15 history answered Stefan Waldmann CC BY-SA 2.5