Definition 5.28.3. Let $X$ be a topological space. A *stratification* of $X$ is given by a partition $X = \coprod _{i \in I} X_ i$ and a partial ordering on $I$ such that for each $j \in I$ we have

\[ \overline{X_ j} \subset \bigcup \nolimits _{i \leq j} X_ i \]

The parts $X_ i$ are called the *strata* of the stratification.

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