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- Title
Spectral subspaces of spectra of Abelian lattice-ordered groups in size aleph one.
- Authors
Ploščica, Miroslav; Wehrung, Friedrich
- Abstract
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; yet 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 with at most ℵ 1 compact open sets is homeomorphic to a spectral subspace of the ℓ -spectrum of some Abelian ℓ -group.
- Subjects
ABELIAN groups; GENERALIZED spaces; HOMOMORPHISMS; RIESZ spaces; HEYTING algebras
- Publication
Acta Scientiarum Mathematicarum, 2023, Vol 89, Issue 3/4, p339
- ISSN
0001-6969
- Publication type
Article
- DOI
10.1007/s44146-023-00080-z