The Stacks project

Definition 5.11.4. Let $X$ be a topological space. We say $X$ is catenary if for every pair of irreducible closed subsets $T \subset T'$ we have $\text{codim}(T, T') < \infty $ and every maximal chain of irreducible closed subsets

\[ T = T_0 \subset T_1 \subset \ldots \subset T_ e = T' \]

has the same length (equal to the codimension).

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View Definition 5.11.4 as pdf