# Are the two formulations of Baire category theorem equivalent for arbitrary metric spaces?

As we all know, Baire Category theorem has two equivalent forms

1. $$X$$ is a complete metric space, then the countable intersection of dense open sets is nonempty.
2. $$X$$ is a complete metric space, $$X$$ is a second category set.

Two forms are equivalent if $$X$$ is complete. If $$X$$ is a general metric space, are they still equivalent?

$$X$$ is a Baire space iff $$X$$ is second category in itself.