Another proof of Banaschewski's surjection theorem

نویسندگان
Baboolal, Dharmanand ID 1
Pultr, Ales ID 2
Picado, Jorge ID 3

1 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000, South Africa.

2 Department of Applied Mathematics and ITI, MFF, Charles University, Malostranske nam. 24, 11800 Praha 1, Czech Republic

3 Department of Mathematics University of Coimbra PORTUGAL

doi
10.29252/cgasa.11.1.113
چکیده

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.

کلیدواژه‌ها
Frame (locale), sublocale, uniform frame, quasi-uniform frame, uniform embedding, complete uniform frame, completion, Cauchy map, Cauchy filter, Cauchy complete