Hi everyone: Suppose $E\subset \mathbb{R}^{n}$ is a closed set with empty interior, and $ D $ a domain in $\mathbb{C}^{n}$ with $n\geq2$. Can we conclude that the open set $ D\setminus E $ is connected?
Can this "real set" disconnect complex n-space?
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general-topology
complex-analysis
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0E is a real set? What is this difference? – 2017-01-09
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0do you mean that we should view $D$ as a subset of $\mathbb R ^{2n}$? – 2017-01-09
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7Well, even $\mathbb C^n\setminus \mathbb R^n$ is connected when $n\ge 2$ ... – 2017-01-09
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0The set $E$ is inside $\lbrace z=x+i0: x\in\mathbb{R}^{n}$. We can consider $D$ as part of $ \mathbb{R}^{n} $. – 2017-01-09
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0Henning Makholm: I think you are right, but how would you prove it? – 2017-01-09