Definition 5.11.4 (02I1)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 5: Topology
Section 5.11: Codimension and catenary spaces
Definition 5.11.4 (cite)

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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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