Journal of Integer Sequences, Vol. 13 (2010), Article 10.3.5

Finite Topologies and Partitions

Moussa Benoumhani* and Messaoud Kolli
Faculty of Science
Department of Mathematics
King Khaled University
Saudi Arabia

* Author's current address: Department of Mathematics, Al-Imam University, Faculty of Sciences, P. O. Box 90950, Riyadh 11623, Saudi Arabia.


Let E be a set with n elements, and let T(n,k) be the number of all labeled topologies having k open sets that can be defined on E. In this paper, we compute these numbers for k ≤ 17, and arbitrary n, as well as tN0(n,k), the number of all unlabeled non-T0 topologies on E with k open sets, for 3 ≤ k ≤ 8.

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(Concerned with sequences A000798 A001930 A008277 A122934.)

Received September 11 2007; revised versions received October 18 2007; July 7 2009; January 19 2010; March 6 2010. Published in Journal of Integer Sequences, March 10 2010. Minor revision, March 18 2010. Added author's new address, December 1 2010.

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