Definition 2

Tag 09GA, permanent. Cite it as [Bourbaki, Tag 09GA].

Integration, VII, p. 51, § 2. Quotient of a space by a group; homogeneous spaces

Let $F \subset X$ . One says that $F$ is a fundamental domain (for $H$ ) if the restriction of $\pi$ to $F$ is a bijection of $F$ onto $X/H$ (in other words, $F$ is a system of representatives for the equivalence relation defined by $H$ ).

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

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