Weight of a topological space

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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.


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