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Title: Another proof of Banaschewski's surjection theorem
Authors: Baboolal, Dharmanand
Picado, Jorge 
Pultr, Aleš 
Keywords: Frame (locale); sublocale; uniform frame; quasi-uniform frame; uniform embedding; complete uniform frame; completion; Cauchy map; Cauchy filter; Cauchy complete.
Issue Date: 2019
Publisher: Shahid Beheshti University
Project: UID/MAT/00324/2013 
Serial title, monograph or event: Categories and General Algebraic Structures with Applications
Volume: 11
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.
ISSN: 2345-5853
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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