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I was reading III vol. of Princeton lectures on analysis. Proposition 1.4: "If $\Omega_{1}\supset\Omega_{2}\supset\ldots\supset\Omega_{n}\supset\ldots $ is a sequence of non-empty compact sets in $\Bbb C$ with the property that: $$\operatorname{diam}(\Omega_{n})\to 0\text{ as } n\to\infty,$$ th...