Definition 5.15.1. Let $X$ be a topological space. Let $E \subset X$ be a subset of $X$.

1. We say $E$ is constructible1 in $X$ if $E$ is a finite union of subsets of the form $U \cap V^ c$ where $U, V \subset X$ are open and retrocompact in $X$.

2. We say $E$ is locally constructible in $X$ if there exists an open covering $X = \bigcup V_ i$ such that each $E \cap V_ i$ is constructible in $V_ i$.

[1] In the second edition of EGA I this was called a “globally constructible” set and a the terminology “constructible” was used for what we call a locally constructible set.

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