Definition 5.28.1. Let $X$ be a topological space. A *partition* of $X$ is a decomposition $X = \coprod X_ i$ into locally closed subsets $X_ i$. The $X_ i$ are called the *parts* of the partition. Given two partitions of $X$ we say one *refines* the other if the parts of one are unions of parts of the other.

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