Weight of a topological space
From Encyclopedia of Mathematics - Reading time: 1 min
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[edit]
| [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 |
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