, Volume 27, Issue 4, pp 2851-2854

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

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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.

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 32–36, 1982.