• Corpus ID: 249926773

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

  title={Spectral subspaces of spectra of Abelian lattice-ordered groups in size aleph one},
  author={Miroslav Plo{\vs}{\vc}ica and Friedrich Wehrung},
. 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… 



Cevian properties in ideal lattices of Abelian ℓ-groups

Abstract We consider the problem of describing the lattices of compact ℓ{\ell}-ideals of Abelian lattice-ordered groups. (Equivalently, describing the spectral spaces of Abelian lattice-ordered

Spectral spaces of countable Abelian lattice-ordered groups

  • F. Wehrung
  • Mathematics
    Transactions of the American Mathematical Society
  • 2018
A compact topological space X is spectral if it is sober (i.e., every irreducible closed set is the closure of a unique singleton) and the compact open subsets of X form a basis of the topology of X,

Free vector lattices

An investigation into the algebraic properties of free objects in the category of vector lattices is carried out. It is shown that each ideal of a free vector lattice is a cardinal (direct) sum of

Real Spectrum Versus ℓ-Spectrum via Brumfiel Spectrum

  • F. Wehrung
  • Mathematics
    Algebras and Representation Theory
  • 2021
It is well known that the real spectrum of any commutative unital ring, and the l-spectrum of any Abelian lattice-ordered group with order-unit, are all completely normal spectral spaces. We prove

The essential cover and the absolute cover of a schematic space

A theorem of Gleason states that every compact space admits a projective cover. More generally, in the category of topological spaces with continuous maps, covers exist with respect to the full

From noncommutative diagrams to anti-elementary classes

It is proved that many naturally defined classes are anti-elementary, including the class of all lattices of finitely generated convex l-subgroups of members of any class of l- groups containing all Archimedean l-groups.

From Objects to Diagrams for Ranges of Functors

Let A, B, S be categories, let F:A-->S and G:B-->S be functors. We assume that for ''many'' objects a in A, there exists an object b in B such that F(a) is isomorphic to G(b). We establish a general

Advanced Łukasiewicz calculus and MV-algebras

This book discusses the construction of free products of MV-algebras, the spectral and the maximal spectral space, and a first-order Lukasiewicz logic with [0, 1]-identity.