Prime spectra of lattice-ordered abelian groups
We prove that for each ℓ-group G, the topological space Spec(G) satisfies a condition Idω. Generalising a previous construction of Delzell and Madden we show that for each nondenumerable cardinal there is a completely normal spectral space that is not homeomorphic to Spec(G) for any ℓ-group G. We sh...
| Autores principales: | , , |
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| Formato: | Artículo publishedVersion |
| Lenguaje: | Inglés |
| Publicado: |
1999
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00224049_v136_n3_p217_Cignoli |
| Aporte de: |
| Sumario: | We prove that for each ℓ-group G, the topological space Spec(G) satisfies a condition Idω. Generalising a previous construction of Delzell and Madden we show that for each nondenumerable cardinal there is a completely normal spectral space that is not homeomorphic to Spec(G) for any ℓ-group G. We show also that a stronger form of property Idω, called Id, suffices to ensure that a completely normal spectral space is homeomorphic to Spec(G) for some ℓ-group G. © 1999 Elsevier Science B.V. All rights reserved. |
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