• Corpus ID: 249926773

# Spectral subspaces of spectra of Abelian lattice-ordered groups in size aleph one

@inproceedings{Ploica2022SpectralSO,
title={Spectral subspaces of spectra of Abelian lattice-ordered groups in size aleph one},
author={Miroslav Plo{\vs}{\vc}ica and Friedrich Wehrung},
year={2022}
}
• Published 20 June 2022
• Mathematics
. It is well known that the lattice Id c G of all principal ℓ -ideals of any Abelian ℓ -group G is a completely normal distributive 0-lattice, and that not every completely normal distributive 0-lattice is a homomorphic image of some Id c G , via a counterexample of cardinality ℵ 2 . We prove that every completely normal distributive 0-lattice with at most ℵ 1 elements is a homomorphic image of some Id c G . By Stone duality, this means that every completely normal generalized spectral space…

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