# Definition:Character of Point in Topological Space

## Definition

Let $T$ be a topological space.

Let $x$ be a point of $T$.

Let $\mathbb B \left({x}\right)$ 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 $\mathbb B \left({x}\right)$:

$\chi \left({x,T}\right) := \min \left\{ {\left\vert{\mathcal B}\right\vert: \mathcal B \in \mathbb B \left({x}\right)}\right\}$