uu.seUppsala University Publications

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The Vitali covering theorem in constructive mathematicsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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(English)Article in journal (Refereed) Submitted
##### Abstract [en]

##### Keywords [en]

Constructive mathematics, Reverse mathematics, Measure theory, Vitali's covering theorem, Formal topology
##### Research subject

Mathematical Logic
##### Identifiers

URN: urn:nbn:se:uu:diva-152066OAI: oai:DiVA.org:uu-152066DiVA, id: diva2:412413
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt446",{id:"formSmash:j_idt446",widgetVar:"widget_formSmash_j_idt446",multiple:true}); Available from: 2011-04-22 Created: 2011-04-22 Last updated: 2011-06-14Bibliographically approved
##### In thesis

This paper investigates the Vitali Covering Theorem from various constructive angles. A Vitali Cover of a metric space is a cover such that for every point there exists an arbitrarily small set of the cover containing this point. The VCT now states, that for any Vitali Cover one can find a finite, disjoint family of sets in the Vitali Cover that cover the entire space up to a set of a given non-zero measure. We will show, by means of a recursive counterexample, that there cannot be a fully constructive proof, but that adding a very weak semi-constructive principle suffices to give such a proof. Lastly, we will show that with an appropriate formalization in formal topology the non-constructive problems can be avoided completely.

1. Contributions to Pointfree Topology and Apartness Spaces$(function(){PrimeFaces.cw("OverlayPanel","overlay412415",{id:"formSmash:j_idt720:0:j_idt724",widgetVar:"overlay412415",target:"formSmash:j_idt720:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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