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Article Dans Une Revue Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum Année : 2023

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

Résumé

It is well known that the lattice Idc 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 Idc 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 Idc G. By Stone duality, this means that every completely normal generalized spectral space, with at most ℵ 1 compact open sets, is homeomorphic to a spectral subspace of the ℓ-spectrum of some Abelian ℓ-group.
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Dates et versions

hal-03696927 , version 1 (16-06-2022)

Identifiants

Citer

Miroslav Ploščica, Friedrich Wehrung. Spectral subspaces of spectra of Abelian lattice-ordered groups in size aleph one. Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum, 2023, 89 (3-4), pp.339--356. ⟨10.1007/s44146-023-00080-z⟩. ⟨hal-03696927⟩
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