Another proof of Banaschewski's surjection theorem

• Autor(a) principal: Baboolal, Dharmanand
• Data de Publicação: 2019
• Outros Autores: Picado, Jorge, Pultr, Aleš
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/90470
• topic: Frame (locale); sublocale; uniform frame; quasi-uniform frame; uniform embedding; complete uniform frame; completion; Cauchy map; Cauchy filter; Cauchy complete.

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.