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Proceedings of the American Mathematical Society

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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.

References [Enhancements On Off] (What's this?)

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Keywords: Partial order, finite set, asymptotic enumeration
Article copyright: © Copyright 1970 American Mathematical Society