The Stacks project

Remark 26.12.6. Let $X$ be a scheme. Let $T \subset X$ be a locally closed subset. In this situation we sometimes also use the phrase “reduced induced scheme structure on $T$”. It refers to the reduced induced scheme structure from Definition 26.12.5 when we view $T$ as a closed subset of the open subscheme $X \setminus \partial T$ of $X$. Here $\partial T = \overline{T} \setminus T$ is the “boundary” of $T$ in the topological space of $X$.