Constructive pointfree topology eliminates non-constructive representation theorems from Riesz space theory
Functional Analysis
2010-05-26 v1 Logic
Abstract
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.
Keywords
Cite
@article{arxiv.0807.2454,
title = {Constructive pointfree topology eliminates non-constructive representation theorems from Riesz space theory},
author = {Bas Spitters},
journal= {arXiv preprint arXiv:0807.2454},
year = {2010}
}