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Integrals and valuations
, 2008
"... We construct a homeomorphism between the compact regular locale of integrals on a Riesz space and the locale of (valuations) on its spectrum. In fact, we construct two geometric theories and show that they are biinterpretable. The constructions are elementary and mostly consist of explicit manipul ..."
Abstract

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We construct a homeomorphism between the compact regular locale of integrals on a Riesz space and the locale of (valuations) on its spectrum. In fact, we construct two geometric theories and show that they are biinterpretable. The constructions are elementary and mostly consist of explicit manipulations on a distributive lattice associated to a given Riesz space.
Some constructive roads to Tychonoff
 From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics, number 48 in Oxford Logic Guides
, 2005
"... iv ..."
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