Journal of Integer Sequences, Vol. 10 (2007), Article 07.3.1

Direct and Elementary Approach to Enumerate Topologies on a Finite Set

Messaoud Kolli
Faculty of Science
Department of Mathematics
King Khaled University
Saudi Arabia


Let $ \mathbb{E}$ be a set with $ n$ elements, and let $ \tau (n,k)$ be the set of all labelled topologies on $ \mathbb{E}$, having $ k$ open sets, and $ T(n,k)=\left\vert \tau (n,k)\right\vert $. In this paper, we use a direct approach to compute $ T(n,k)$ for all $ n\geq
4$ and $ k\geq 6\cdot 2^{n-4}$.

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(Concerned with sequences A000798, A001930, and A008277 .)

Received April 19 2006; revised version received February 28 2007. Published in Journal of Integer Sequences March 19 2007.

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