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A note on quasi-uniform continuity
Published online by Cambridge University Press: 17 April 2009
Abstract
It is shown that:
(i) a continuous function from a compact quasi-uniform space into a quasi-uniform space is not necessarily quasiuniformly continuous;
(ii) if the range of the function is a uniform space, the function will be necessarily quasi-uniformly continuous.
(This contradicts an example in the literature and generalizes a classical result.) Finally, a generalization of (ii) is given by means of a suitable boundedness notion.
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- Copyright © Australian Mathematical Society 1973
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