Definition:Weight of Topological Space/Definition 2

Definition
Let $T$ be a topological space.

Let $\mathbb B$ be the set of all bases of $T$.

The weight of $T$ is the smallest cardinality of the elements of $\mathbb B$:
 * $w \left({T}\right) := \min \left\{ {\left\vert{\mathcal B}\right\vert: \mathcal B \in \mathbb B}\right\}$

Also see

 * Equivalence of Definitions of Weight of Topological Space