Difference between revisions of "Character (of a topological space)"
From Encyclopedia of Mathematics
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| + | 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. | ||
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| + | A space satisfies the [[first axiom of countability]] if and only if it has countable character. | ||
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| + | ====References==== | ||
| + | * Mary Ellen Rudin, ''Lectures on Set Theoretic Topology'', American Mathematical Society (1975) ISBN 0-8218-1673-X {{ZBL|0318.54001}} | ||
Revision as of 20:05, 31 December 2017
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.
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=42654
Character (of a topological space). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Character_(of_a_topological_space)&oldid=42654