Character (of a topological space)
From Encyclopedia of Mathematics
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