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Resolution of the uniform lower bound problem in constructive analysis
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic. (Mathematical Logic)
2008 (English)In: Mathematical logic quarterly, ISSN 0942-5616, E-ISSN 1521-3870, Vol. 54, no 1, 65-69 p.Article in journal (Refereed) Published
Abstract [en]

In a previous paper we constructed a full and faithful functor M from the category of locally compact metric spaces to the category of formal topologies (representations of locales). Here we show that for a real-valued continuous function f,M (f) factors through the localic positive reals if, and only if, f has a uniform positive lower bound on each ball in the locally compact space. We work within the framework of Bishop constructive mathematics, where the latter notion is strictly stronger than point-wise positivity.

Place, publisher, year, edition, pages
2008. Vol. 54, no 1, 65-69 p.
National Category
Algebra and Logic
Research subject
Mathematical Logic
URN: urn:nbn:se:uu:diva-106108DOI: 10.1002/malq.200710034ISI: 000253551100008OAI: oai:DiVA.org:uu-106108DiVA: diva2:223898
Available from: 2009-06-15 Created: 2009-06-15 Last updated: 2011-03-24Bibliographically approved

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