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Possible Duplicate:
question related to perfect maps preserving compactness

Let $Z$ be a compact topological space and let $Y$ be a topological space. Let $f:Y \rightarrow Z$ be a surjective continuous map so that the preimages of points are always compact. Does $Y$ have to be compact?

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    This was [asked and answered recently](http://math.stackexchange.com/questions/90937/question-related-to-perfect-maps-preserving-compactness).2011-12-14

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