# A compact $G_\delta$ and zero sets. [closed]

Does the following statement true or not and why? A closed $G_\delta$ of a compact space is zero set of a continuous real-valued function.

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## closed as off-topic by Ricardo Andrade, j.c., Andrey Rekalo, Daniel Moskovich, Stefan KohlFeb 5 at 9:53

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• "This question does not appear to be about research level mathematics within the scope defined in the help center." – Ricardo Andrade, j.c., Andrey Rekalo, Daniel Moskovich, Stefan Kohl
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Yes, it is true. In a compact Hausdorff space, "zero set" is the same as "compact $G_\delta$". Since it is a homework type problem, instead of providing a proof I should ask what you have so far...