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Is it possible for the following to hold in metric spaces? Let (X,d) be a metric space,if A is closed in Y and Y is closed in X then A is closed in X. If possible someone could assist me for a proof. Here I try:Since A is closed in Y, then I want to write A=U∩Y, where U is closed in X. But Y is closed in X,hence A is the intersection of two closed sets in X.Can this be applied here? Thanks

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    I've tried to make the title more descriptive - I hope you don't mind. I believe having good title is important, see [How can I ask a good question?](http://meta.math.stackexchange.com/questions/588/how-can-i-ask-a-good-question).2012-04-17
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    Your proof is OK. Congratulations2012-04-17

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