\begin{definition}[Definition:Character of Point in Topological Space]
Let $T$ be a topological space.
Let $x$ be a point of $T$.
Let $\map {\mathbb B} x$ be the set of all local bases at $x$.
The '''character of (the point) $x$ in $T$''' is the smallest cardinality of the elements of $\map {\mathbb B} x$:
:$\map \chi {x, T} := \min \set {\card \BB: \BB \in \map {\mathbb B} x}$
\end{definition}