Remark 5.28.5. Given a locally finite stratification $X = \coprod X_ i$ of a topological space $X$, we obtain a family of closed subsets $Z_ i = \bigcup _{j \leq i} X_ j$ of $X$ indexed by $I$ such that

Conversely, given closed subsets $Z_ i \subset X$ indexed by a partially ordered set $I$ such that $X = \bigcup Z_ i$, such that every point has a neighbourhood meeting only finitely many $Z_ i$, and such that the displayed formula holds, then we obtain a locally finite stratification of $X$ by setting $X_ i = Z_ i \setminus \bigcup _{j < i} Z_ j$.

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