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

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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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     author = {Fletcher, P.},
     title = {Finite {Topological} {Spaces} and {Quasi-Uniform} {Structures}},
     journal = {Canadian mathematical bulletin},
     pages = {771--775},
     year = {1969},
     volume = {12},
     number = {6},
     doi = {10.4153/CMB-1969-099-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-099-9/}
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