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