%0 Journal Article
%T Another proof of Banaschewski's surjection theorem
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Baboolal, Dharmanand
%A Picado, Jorge
%A Pultr, Ales
%D 2019
%\ 07/01/2019
%V 11
%N Special Issue Dedicated to Prof. George A. Grätzer
%P 113-130
%! Another proof of Banaschewski's surjection theorem
%K Frame (locale)
%K sublocale
%K uniform frame
%K quasi-uniform frame
%K uniform embedding
%K complete uniform frame
%K completion
%K Cauchy map
%K Cauchy filter
%K Cauchy complete
%R 10.29252/cgasa.11.1.113
%X 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.
%U https://cgasa.sbu.ac.ir/article_76726_f134d7becf0d86ec81e2ee5972440080.pdf