TITLE: Is there a Baire Category Theorem for Complete Topological Vector Spaces?
QUESTION [8 upvotes]: Baire category theorem is usually proved in the setting of a complete metric space or a locally compact Hausdorff space.
Is there a version of Baire category Theorem for complete topological vector spaces? What other hypotheses might be required?

REPLY [6 votes]: According to Birkhoff-Kakutani theorem, a topological vector space is metrisable if and only if it is Hausdorff and $0$ has a countable neighborhood basis.  (For a topological vector space, being Hausdorff is equivalent to $\{0\}$ being closed.)
Therefore, a complete topological vector space in which $\{0\}$ is closed and $0$ has a countable neighborhood basis satisfies the Baire category theorem.