= Solution
A <closed immersion> $i:X\to Y$ is a <morphism of schemes> whose underlying map is a homeomorphism onto a closed subset and whose map of <structure sheaves>
$$
\mathcal O_Y\longrightarrow i_*\mathcal O_X
$$
is surjective. Equivalently, $X$ is the <closed subscheme> defined by a quasi-coherent <ideal sheaf of a closed subscheme> on $Y$. The affine-local characterization is particularly useful: for every <affine open subscheme> $V=\operatorname{Spec}A\subseteq Y$,
$$
\boxed{i^{-1}(V)\simeq\operatorname{Spec}(A/I)\longrightarrow\operatorname{Spec}A}
$$
for an ideal $I\subseteq A$, with the map induced by the quotient homomorphism.
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