\begin{definition}[Definition:Krull Dimension of Topological Space]
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 inclusion.
Thus, the '''Krull dimension''' is $\infty$ if there exist arbitrarily long chains.
\end{definition}