# Weight of a topological space

From Encyclopedia of Mathematics

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

The smallest cardinal number which is the cardinality of an open base of a topological space. The weight, together with the cardinality, is the most important cardinal invariant of a topological space.

A space satisfies the second axiom of countability if and only if it has countable weight.

#### References

[a1] | A.V. Arkhangel'skii, "Topological function spaces" , Kluwer (1991) (Translated from Russian) |

[a2] | I. Juhász, "Cardinal functions in topology" , North-Holland (1971) |

[a3] | 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:**

Weight of a topological space.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Weight_of_a_topological_space&oldid=42662

This article was adapted from an original article by P.S. Aleksandrov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article