Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585311Special Issue Dedicated to Prof. George A. Grätzer20190701Another proof of Banaschewski's surjection theorem1131307672610.29252/cgasa.11.1.113ENDharmanand BaboolalSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000, South Africa.0000-0001-6737-1656Jorge PicadoDepartment of Mathematics
University of Coimbra
PORTUGAL0000-0001-7837-1221Ales PultrDepartment of Applied Mathematics and ITI, MFF, Charles University,
Malostranske nam. 24, 11800 Praha 1, Czech Republic0000-0002-9308-3700Journal Article20180617We 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.https://cgasa.sbu.ac.ir/article_76726_f134d7becf0d86ec81e2ee5972440080.pdf