Weight of a topological space
From Encyclopedia of Mathematics
Revision as of 20:07, 31 December 2017 by Richard Pinch (talk | contribs) (relation to second countability)
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
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