View source for Character (of a topological space)

{{TEX|done}}{{MSC|54A25}}

One of the [[cardinal characteristic]]s of a [[topological space]] $X$.  The ''local character'' $\chi(x,X)$ at a point $x \in X$ is the least cardinality of a [[local base]] at $x$.  The character $\chi(X)$ is the least upper bound of the local characters.

A space satisfies the [[first axiom of countability]] if and only if it has countable character.


====References====
* Mary Ellen Rudin, ''Lectures on Set Theoretic Topology'', American Mathematical Society (1975) {{ISBN|0-8218-1673-X}} {{ZBL|0318.54001}}