Character (of a topological space)

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2020 Mathematics Subject Classification: Primary: 54A25 [MSN][ZBL]

One of the cardinal characteristics 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.


  • Mary Ellen Rudin, Lectures on Set Theoretic Topology, American Mathematical Society (1975) ISBN 0-8218-1673-X Zbl 0318.54001
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