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Difference between revisions of "Weight of a topological space"

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(MSC 54A25)
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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"> A.V. Arkhangel'skii,   "Topological function spaces" , Kluwer (1991) (Translated from Russian)</TD></TR>
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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>
<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">[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>
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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}} {{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
This article was adapted from an original article by P.S. Aleksandrov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article