# Character (of a topological space)

From Encyclopedia of Mathematics

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2010 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.

#### References

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

**How to Cite This Entry:**

Character (of a topological space).

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Character_(of_a_topological_space)&oldid=42661