Definition:Weight of Topological Space

Definition
Let $T$ be a topological space.

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

The weight of $T$ is defined as:
 * $\displaystyle w \left({T}\right) := \bigcap_{\mathcal B \in \mathbb B} \left\vert {\mathcal B} \right\vert$

where $\left\vert {\mathcal B} \right\vert$ denotes the cardinality of $\mathcal B$.

The weight of $T$ is the minimal cardinality of a basis of $T$.