Constructive pointfree topology eliminates non-constructive representation theorems from Riesz space theory

Details Constructive pointfree topology eliminates non-constructive representation theorems from Riesz space theory Constructive pointfree topology eliminates non-constructive representation theorems from Riesz space theory

2008-07-15

arxiv.org/abs/0807.2454v1

Mathematics

Functional Analysis

Scientific paper

10.1007/s11083-010-9147-3

In Riesz space theory it is good practice to avoid representation theorems which depend on the axiom of choice. Here we present a general methodology to do this using pointfree topology. To illustrate the technique we show that almost f-algebras are commutative. The proof is obtained relatively straightforward from the proof by Buskes and van Rooij by using the pointfree Stone-Yosida representation theorem by Coquand and Spitters.

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