Lemma 27.11.3. Let $S$ be a locally Noetherian scheme. The following are equivalent:

$S$ is catenary, and

locally in the Zariski topology there exists a dimension function on $S$ (see Topology, Definition 5.20.1).

Lemma 27.11.3. Let $S$ be a locally Noetherian scheme. The following are equivalent:

$S$ is catenary, and

locally in the Zariski topology there exists a dimension function on $S$ (see Topology, Definition 5.20.1).

**Proof.**
This follows from Topology, Lemmas 5.11.5, 5.20.2, and 5.20.4, Schemes, Lemma 25.11.1 and finally Lemma 27.5.5.
$\square$

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