\begin{definition}[Definition:Local Dimension of Topological Space]
Let $X$ be a topological space.
Let $x \in X$.
The '''local dimension of $X$ at $x$''' is the supremum of lengths of chains of closed irreducible sets of $T$ containing $x$, ordered by inclusion.
Thus, the '''Krull dimension''' is $\infty$ {{iff}} there exist arbitrarily long chains containing $x$.
\end{definition}