Definition:Character of Point in Topological Space

Definition
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 $\map {\mathbb B} x$:
 * $\map \chi {x, T} := \min \set {\card \BB: \BB \in \map {\mathbb B} x}$