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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0253944-9
MathSciNet review:
0253944
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Abstract | References | Similar Articles | Additional Information
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.
- 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 Company, 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 https://doi.org/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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Additional Information
Keywords:
Partial order,
finite set,
asymptotic enumeration
Article copyright:
© Copyright 1970
American Mathematical Society