Definition 65.47.4. Let $S$ be a scheme. Let $\varphi $ be a rational map between two algebraic spaces $X$ and $Y$ over $S$. We say $\varphi $ is *defined in a point $x \in |X|$* if there exists a representative $(U, f)$ of $\varphi $ with $x \in |U|$. The *domain of definition* of $\varphi $ is the set of all points where $\varphi $ is defined.

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