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Title

Another proof of Banaschewski's surjection theorem

Year: 1398
COI: JR_CGASAT-11-0_005
Language: EnglishView: 27
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Authors

Dharmanand Baboolal - School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban ۴۰۰۰, South Africa.
Jorge Picado - Department of Mathematics University of Coimbra PORTUGAL
Ales Pultr - Department of Applied Mathematics and ITI, MFF, Charles University, Malostranske nam. ۲۴, ۱۱۸۰۰ Praha ۱, Czech Republic

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.

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Paper COI Code

This Paper COI Code is JR_CGASAT-11-0_005. Also You can use the following address to link to this article. This link is permanent and is used as an article registration confirmation in the Civilica reference:

https://civilica.com/doc/1267963/

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If you want to refer to this Paper in your research work, you can simply use the following phrase in the resources section:
Baboolal, Dharmanand and Picado, Jorge and Pultr, Ales,1398,Another proof of Banaschewski's surjection theorem,https://civilica.com/doc/1267963

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  • Banaschewski, B., Uniform completion in pointfree topology, In: Rodabaugh S.E., ...
  • Banaschewski, B., Hong, S.S., and Pultr, A., On the completion ...
  • Banaschewski, B. and Pultr, A., Samuel compactification and completion of ...
  • Banaschewski, B. and Pultr, A., Cauchy points of uniform and ...
  • Isbell, J.R., “Uniform Spaces”, Amer. Math. Soc., ۱۹۶۴ ...
  • Johnstone, P.T., “Stone Spaces”, Cambridge University Press, ۱۹۸۲ ...
  • Kelley, J.L., “General Topology”, D. Van Nostrand Co., ۱۹۵۵ ...
  • Kríž, I., A direct description of uniform completion in locales ...
  • Picado, J., Weil uniformities for frames, Comment. Math. Univ. Carolin. ...
  • Picado, J., Structured frames by Weil entourages, Appl. Categ. Structures ...
  • Picado, J. and Pultr, A., “Frames and locales: Topology without ...
  • Picado, J. and Pultr, A., Entourages, covers and localic groups, ...
  • Picado, J. and Pultr, A., Entourages, density, Cauchy maps, and ...
  • Pultr, A., Pointless uniformities I, Comment. Math. Univ. Carolin. ۲۵ ...
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