Definition:Weight of Topological Space
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Definition
Let $T$ be a topological space.
Let $\mathbb B$ be the set of all bases of $T$.
Definition 1
The weight of $T$ is defined as:
- $\ds \map w T := \bigcap_{\BB \mathop \in \mathbb B} \card \BB$
where $\card \BB$ denotes the cardinality of $\BB$.
Definition 2
The weight of $T$ is the smallest cardinality of the elements of $\mathbb B$:
- $\map w T := \min \set {\card \BB: \BB \in \mathbb B}$