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On topological spaces with a unique compatible quasi-uniformity
Published online by Cambridge University Press: 18 May 2009
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It is shown in [2] that a uqu space satisfies the following conditions.
(DC) There is no infinite, strictly decreasing sequence of open sets with open intersection.
(IC) There is no infinite, strictly increasing sequence of open sets.
In this note we show that for a transitive space these conditions are sufficient for the space to be uqu. This will follow as a consequence of the following result.
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- Copyright © Glasgow Mathematical Journal Trust 1977
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