Character (of a topological space)
From Encyclopedia of Mathematics
Revision as of 20:05, 31 December 2017 by Richard Pinch (talk | contribs) (Start article: Character (of a topological space))
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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=42661
Character (of a topological space). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Character_(of_a_topological_space)&oldid=42661