= Solution
A <rational map> from <irreducible topological space>[irreducible] $X$ to $Y$ is an equivalence class of <morphism of varieties>[morphisms] $F_U:U\to Y$ defined on nonempty <open subsets> $U\subseteq X$. Two representatives are equivalent if they agree on a nonempty <open subset> of their <intersection>.
<irreducible topological space>[Irreducibility] makes all these nonempty opens <dense> and ensures their <intersections> are nonempty, so the equivalence expresses agreement at general <points>. A <rational map> need not extend across all of $X$, and it need not be dominant. An <injective> <homomorphism> of <function fields> additionally requires a <dominant morphism of affine varieties>, or the corresponding condition on a <rational map>.
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