Corpus ID: 235266073

Uniform locales and their constructive aspects

  title={Uniform locales and their constructive aspects},
  author={Graham Manuell},
Much work has been done on generalising results about uniform spaces to the pointfree context. However, this has almost exclusively been done using classical logic, whereas much of the utility of the pointfree approach lies in its constructive theory, which can be interpreted in many different toposes. Johnstone has advocated for the development of a constructive theory of uniform locales and wrote a short paper on the basic constructive theory via covering uniformities, but he never followed… Expand


Localic completion of uniform spaces
  • Tatsuji Kawai
  • Mathematics, Computer Science
  • Log. Methods Comput. Sci.
  • 2017
It is shown that the localic completion of a symmetric gus is equivalent to the point-free completion of the uniform formal topology associated with the gus, which simplifies the existing characterisation for metric spaces. Expand
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The coreflection theorem states that open locales are coreflective in locales and hence, as a consequence of well-known impredicative results on exponentiable locales, it allows to prove that locally compact openLocales are exponentiable in the category ofopen locales. Expand
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On the collection of points of a formal space
  • G. Curi
  • Mathematics, Computer Science
  • Ann. Pure Appl. Log.
  • 2006
Abstract The collection of points of a locally compact regular formal space is shown to be isomorphic to a set in the context of Martin-Lof type theory. By introducing the notion of uniform formalExpand