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What can we say about the product space (with product topology) $X\times Y$ if $X$ is an arbitrary topological space and $Y$ is a compact Hausdorff space?

Do we know from the given information if the projection $\pi:X\times Y\to X$ is open/closed?

Regards

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    The projections for a product space are always open.2012-02-02
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    Related: http://math.stackexchange.com/questions/22697/projection-map-being-a-closed-map2012-02-02

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