# Definition:Krull Dimension of Topological Space

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## Definition

Let $T$ be a topological space.

Its **Krull dimension** $\map {\dim_{\mathrm {Krull} } } T$ is the supremum of lengths of chains of closed irreducible sets of $T$, ordered by the subset relation.

Thus, the **Krull dimension** is $\infty$ if there exist arbitrarily long chains.

## Also denoted as

The **Krull dimension** can also be denoted $\operatorname {K-dim}$ or simply $\dim$, if there is no confusion.

## Also see

## Source of Name

This entry was named for Wolfgang Krull.