Another proof of Banaschewski's surjection theorem
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Abstract:
We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform sublocale can be extended to a (regular) Cauchy point on the larger (quasi-)uniform frame.
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Journal title
volume 11 issue Special Issue Dedicated to Prof. George A. Grätzer
pages 113- 130
publication date 2019-07-01
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