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Finite Topological Spaces and Quasi-Uniform Structures
Published online by Cambridge University Press: 20 November 2018
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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].
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- Copyright © Canadian Mathematical Society 1969
References
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