Journal of Soviet Mathematics

, Volume 27, Issue 4, pp 2851–2854

Periodicity of residues of the number of finite labeled To-topologies

  • Z. I. Borevich
Article
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Abstract

Let T0(n) be the number of labeled topologies on points satisfying the To separation axiom. It is proved that for any prime p the sequence of residue classes To(n) mod p is periodic with period length p−1.

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Literature cited

  1. 1.
    Z. I. Borevich, “Enumeration of finite topologies,” J. Sov. Math.,20, No. 6 (1982).Google Scholar
  2. 2.
    Z. I. Borevich, “Periodicity of the residues of the number of finite labeled topologies,” J. Sov. Math. (in preparation).Google Scholar
  3. 3.
    L. Comtet, “Recouvrements, bases de filtre et topologies d'un ensemble fini,” C. R. Acad. Sci.,AB262, No. 20, A1091-A1094 (1966).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • Z. I. Borevich

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