Definition:Character of Point in Topological Space

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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 $\map {\mathbb B} x$:

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


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