Reference;
http://www.samos.aegean.gr/math/kker/papers/CompactMetric.pdf
The paper says "Compact metric space is separable" is unprovable in ZF$^0$( That is, ZF without axiom of regularity).
And I know "Limit point compact" does not imply "separable" in ZF
I searched for it, but couldn't find whether "Compact metric space $\Rightarrow$ Separable"
Is it provable in ZF?
Thank you in advance