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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The number of finite topologies
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by D. Kleitman and B. Rothschild
Proc. Amer. Math. Soc. 25 (1970), 276-282
DOI: https://doi.org/10.1090/S0002-9939-1970-0253944-9

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
  • Garrett Birkhoff, Lattice Theory, American Mathematical Society, New York, 1940. MR 0001959
  • S. D. Chatterji, The number of topologies on $n$ points, Kent State University, NASA Technical Report, 1966.
  • Louis Comtet, Recouvrements, bases de filtre et topologies d’un ensemble fini, C. R. Acad. Sci. Paris Sér. A-B 262 (1966), A1091–A1094 (French). MR 201325
  • J. W. Evans, F. Harary and M. S. Lynn, On the computer enumeration of finite topologies, Comm. ACM 10 (1967), 295-298.
  • John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
  • David A. Klarner, The number of graded partially ordered sets, J. Combinatorial Theory 6 (1969), 12–19. MR 236035
  • —, The number of classes of isomorphic graded partially ordered sets, (to appear).
  • V. Krishnamurthy, On the number of topologies on a finite set, Amer. Math. Monthly 73 (1966), 154–157. MR 201324, DOI 10.2307/2313548
  • Oystein Ore, Theory of graphs, American Mathematical Society Colloquium Publications, Vol. XXXVIII, American Mathematical Society, Providence, R.I., 1962. MR 0150753
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 25 (1970), 276-282
  • MSC: Primary 06.20; Secondary 05.00
  • DOI: https://doi.org/10.1090/S0002-9939-1970-0253944-9
  • MathSciNet review: 0253944