# A compact $G_\delta$ and zero sets.

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.

-
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...