Difference between revisions of "Weight of a topological space"
From Encyclopedia of Mathematics
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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 characteristic|cardinal invariant]] of a topological space. | 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 characteristic|cardinal invariant]] of a topological space. | ||
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| + | A space satisfies the [[second axiom of countability]] if and only if it has countable weight. | ||
====References==== | ====References==== | ||
<table> | <table> | ||
| − | <TR><TD valign="top">[a1]</TD> <TD valign="top"> | + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> A.V. Arkhangel'skii, "Topological function spaces" , Kluwer (1991) (Translated from Russian)</TD></TR> |
| − | <TR><TD valign="top">[a2]</TD> <TD valign="top"> | + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> I. Juhász, "Cardinal functions in topology" , North-Holland (1971)</TD></TR> |
| − | <TR><TD valign="top">[a3]</TD> <TD valign="top"> Mary Ellen Rudin, ''Lectures on Set Theoretic Topology'', American Mathematical Society (1975) ISBN 0-8218-1673-X</TD></TR> | + | <TR><TD valign="top">[a3]</TD> <TD valign="top"> Mary Ellen Rudin, ''Lectures on Set Theoretic Topology'', American Mathematical Society (1975) {{ISBN|0-8218-1673-X}} {{ZBL|0318.54001}}</TD></TR> |
</table> | </table> | ||
Latest revision as of 20:48, 5 December 2023
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=35340
Weight of a topological space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Weight_of_a_topological_space&oldid=35340
This article was adapted from an original article by P.S. Aleksandrov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article