Lemma 5.11.6. Let $X$ be a topological space. The following are equivalent:

$X$ is catenary, and

for every pair of irreducible closed subsets $Y \subset Y'$ we have $\text{codim}(Y, Y') < \infty $ and for every triple $Y \subset Y' \subset Y''$ of irreducible closed subsets we have

\[ \text{codim}(Y, Y'') = \text{codim}(Y, Y') + \text{codim}(Y', Y''). \]

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