Finite Topologies and Partitions
Moussa Benoumhani and Messaoud Kolli
Faculty of Science
Department of Mathematics
King Khaled University
Abha
Saudi Arabia
Abstract:
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.
Full version: pdf,
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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.
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