Table of Contents
International Journal of Combinatorics
Volume 2014, Article ID 798074, 7 pages
http://dx.doi.org/10.1155/2014/798074
Research Article

On the Cardinality of the -Topologies on a Finite Set

Department of Mathematics, Faculty of Science, King Khalid University, Abha, Saudi Arabia

Received 7 July 2013; Revised 5 February 2014; Accepted 5 February 2014; Published 31 March 2014

Academic Editor: Laszlo A. Szekely

Copyright © 2014 Messaoud Kolli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be the number of all labeled -topologies having open sets that we can define on points, and let be the number of those which are nonhomeomorphic. In this paper, we compute these numbers for and arbitrary . The numbers of all unlabeled and non- -topologies with open sets are also given for .