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The exercise states "If $X$ is a Noetherian topological space, show that the union of any subset of the connected components of $X$ is always open and closed in $X$."

Does the question mean "If I have some connected components of $X$, then union of those will be open and closed"? or does it mean "If I have some connected components of $X$, take any subset from each component and then the union of those will be open and closed"? Thanks!

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The question mean "If you have some connected components of $X$, then union of those will be open and closed". And the question is to show it is closed, because any union of opens subsets is open.

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