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Does closure of a set mean, only adding boundary values if the set is open and leave it as it is if the set is closed?

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    Don’t forget, there are sets that are neither open nor closed. An example is $\{z\in\Bbb C:1\le|z|<2\}$. To get the closure of such a set, you must include its boundary points, even though it’s not an open set.2012-11-05

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