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Christopher Townsend (2007)
Commentationes Mathematicae Universitatis Carolinae
Given an axiomatic account of the category of locales the closed subgroup theorem is proved. The theorem is seen as a consequence of a categorical account of the Hofmann-Mislove theorem. The categorical account has an order dual providing a new result for locale theory: every compact subgroup is necessarily fitted.
Christopher F. Townsend (2006)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Bernhard Banaschewski, Aleš Pultr (1998)
Commentationes Mathematicae Universitatis Carolinae
We present a unified treatment of pointfree metrization theorems based on an analysis of special properties of bases. It essentially covers all the facts concerning metrization from Engelking [1] which make pointfree sense. With one exception, where the generalization is shown to be false, all the theorems extend to the general pointfree context.
Anders Kock, Gonzalo Reyes (1999)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
A. Pultr, J. Sichler (2000)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Bernhard Banaschewski, Aleš Pultr (2010)
Archivum Mathematicum
A covariant representation of the category of locales by approximate maps (mimicking a natural representation of continuous maps between spaces in which one approximates points by small open sets) is constructed. It is shown that it can be given a Kleisli shape, as a part of a more general Kleisli representation of meet preserving maps. Also, we present the spectrum adjunction in this approximation setting.
Jorge Martinez (2008)
Commentationes Mathematicae Universitatis Carolinae
This paper extends the notion of an archimedean frame to frames which are not necessarily algebraic. The new notion is called joinfitness and is Choice-free. Assuming the Axiom of Choice and for compact normal algebraic frames, the new and the old coincide. There is a subfunctor from the category of compact normal frames with skeletal maps with joinfit values, which is almost a coreflection. Conditions making it so are briefly discussed. The concept of an infinitesimal element arises naturally,...
Siweya, Hlengani James (2002)
International Journal of Mathematics and Mathematical Sciences
Jorge Picado, Aleš Pultr (2019)
Commentationes Mathematicae Universitatis Carolinae
More precisely, we are analyzing some of H. Simmons, S. B. Niefield and K. I. Rosenthal results concerning sublocales induced by subspaces. H. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the role of the axiom for the relation of certain degrees of scatteredness but did not emphasize its role in the relation between sublocales and subspaces. S. B. Niefield and K. I. Rosenthal just mention this axiom in a remark about Simmons’ result. In this...
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