Remark
Tag 0C7B, permanent. Cite it as [Bourbaki, Tag 0C7B].
General Topology, chapter IX, § 5. Baire spaces
There are Baire spaces which belong to neither of these two categories, in particular Baire spaces which are neither metrizable nor locally compact (Exercise 16); there are also metrizable Baire spaces which possess no complete metric space structure compatible with their topology (Exercise 14).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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