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.
closed as off-topic by Ricardo Andrade, j.c., Andrey Rekalo, Daniel Moskovich, Stefan Kohl Feb 5 at 9:53
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "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
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...