Geodesic
Finite Topological Spaces and Quasi-Uniform Structures
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 771-775

Voir la notice de l'article provenant de la source Cambridge University Press

In [6], H. Sharp gives a matrix characterization of each topology on a finite set X = {x1, x2,..., xn}. The study of quasi-uniform spaces provides a more natural and obviously equivalent characterization of finite topological spaces. With this alternate characterization, results of quasi-uniform theory can be used to obtain simple proofs of some of the major theorems of [1], [3] and [6]. Moreover, the class of finite topological spaces has a quasi-uniform property which is of interest in its own right. All facts concerning quasi-uniform spaces which are used in this paper can be found in [4]. 
Fletcher, P. Finite Topological Spaces and Quasi-Uniform Structures. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 771-775. doi: 10.4153/CMB-1969-099-9
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[1] 1. Bonnet, D.A. and Porter, J. R., Matrix characterizations of topological properties. Canad. Math. Bull. 11 (1968) 95–105. Google Scholar

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[3] 3. Krishnamurthy, V., On the number of topologies on a finite set. Amer. Math. Monthly 73 (1966) 154–157. Google Scholar

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