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A constructive and functorial embedding of locally compact metric spaces into locales
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic. (matematisk logik)
2007 (English)In: Topology and its Applications, ISSN 0166-8641, Vol. 154, no 9, 1854-1880 p.Article in journal (Refereed) Published
Abstract [en]

The paper establishes, within constructive mathematics, a full and faithful functor M from the category of locally compact metric spaces and continuous functions into the category of formal topologies (or equivalently locales). The functor preserves finite products, and moreover satisfies f ≤ g if, and only if, M (f) ≤ M (g) for continuous f, g : X → R. This makes it possible to transfer results between Bishop's constructive theory of metric spaces and constructive locale theory.

Place, publisher, year, edition, pages
2007. Vol. 154, no 9, 1854-1880 p.
Keyword [en]
Locales, Formal topologies, Locally compact metric spaces
National Category
URN: urn:nbn:se:uu:diva-13558DOI: 10.1016/j.topol.2007.01.018ISI: 000246688500002OAI: oai:DiVA.org:uu-13558DiVA: diva2:41328
Available from: 2008-01-23 Created: 2008-01-23 Last updated: 2011-01-31Bibliographically approved

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