Corollary

Tag 0C8E, permanent. Cite it as [Bourbaki, Tag 0C8E].

The set of irrational numbers, endowed with the topology induced by that of the real line $\mathbf{R}$ , is a Polish space.

It is the intersection of a countable family of open sets in $\mathbf{R}$ , namely the complements of sets consisting of a single rational number.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.