Resolution of the uniform lower bound problem in constructive analysis
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
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.
Algebra and Logic
Research subject Mathematical Logic
IdentifiersURN: urn:nbn:se:uu:diva-106108DOI: 10.1002/malq.200710034ISI: 000253551100008OAI: oai:DiVA.org:uu-106108DiVA: diva2:223898