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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The number of finite topologies


Authors: D. Kleitman and B. Rothschild
Journal: Proc. Amer. Math. Soc. 25 (1970), 276-282
MSC: Primary 06.20; Secondary 05.00
MathSciNet review: 0253944
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Abstract: The logarithm (base 2) of the number of distinct topologies on a set of $ n$ elements is shown to be asymptotic to $ {n^2}/4$ as $ n$ goes to infinity.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0253944-9
PII: S 0002-9939(1970)0253944-9
Keywords: Partial order, finite set, asymptotic enumeration
Article copyright: © Copyright 1970 American Mathematical Society



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