I have this proposition.
Let X,Y be a metric spaces and let $f:X \to Y$ be a map. Then f is continuous if and only if $f^{-1} (V)$ is closed in X whenever V is closed in Y.
How would you go about proving this?
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Seems a duplicate of http://math.stackexchange.com/q/1511601/4280 (which has no accepter answer...., so I cannot vote for closing as duplicate ) – Henno Brandsma Nov 05 '15 at 22:10
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Do you know the result with "open" instead of "closed"? – zhw. Nov 05 '15 at 22:10
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@HennoBrandsma It would not need an accepted answer, an answer with positive score suffices. – Daniel Fischer Nov 05 '15 at 22:24