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Difference between revisions of "Weight of a topological space"

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The smallest cardinal number which is the cardinality of an open [[Base|base]] of the [[Topological space|topological space]]. The weight, together with the cardinality, is the most important cardinal invariant of a topological space.
 
  
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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.
  
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====Comments====
 
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Cf. also [[Cardinal characteristic|Cardinal characteristic]].
 
  
 
====References====
 
====References====
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<table><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">  I. Juhász,  "Cardinal functions in topology" , North-Holland  (1971)</TD></TR></table>
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<table>
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  A.V. Arkhangel'skii,  "Topological function spaces" , Kluwer  (1991)  (Translated from Russian)</TD></TR>
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<TR><TD valign="top">[a2]</TD> <TD valign="top">  I. Juhász,  "Cardinal functions in topology" , North-Holland  (1971)</TD></TR>
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<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>
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</table>

Revision as of 21:40, 4 December 2014

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.


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
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=32844
This article was adapted from an original article by P.S. Aleksandrov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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