Displaying similar documents to “On iterated limits of subsets of a convergence ℓ -group”

Dieudonné-type theorems for lattice group-valued k -triangular set functions

Antonio Boccuto, Xenofon Dimitriou (2019)

Kybernetika

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Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for k -triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems.

The H S P -Classes of Archimedean l -groups with Weak Unit

Bernhard Banaschewski, Anthony Hager (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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W denotes the class of abstract algebras of the title (with homomorphisms preserving unit). The familiar H , S , and P from universal algebra are here meant in W . ℤ and ℝ denote the integers and the reals, with unit 1, qua W -objects. V denotes a non-void finite set of positive integers. Let 𝒢 ⊆ W be non-void and not { { 0 } } . We show ...

Finitely valued f -modules, an addendum

Stuart A. Steinberg (2001)

Czechoslovak Mathematical Journal

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In an ℓ -group M with an appropriate operator set Ω it is shown that the Ω -value set Γ Ω ( M ) can be embedded in the value set Γ ( M ) . This embedding is an isomorphism if and only if each convex ℓ -subgroup is an Ω -subgroup. If Γ ( M ) has a.c.c. and M is either representable or finitely valued, then the two value sets are identical. More generally, these results hold for two related operator sets Ω 1 and Ω 2 and the corresponding Ω -value sets Γ Ω 1 ( M ) and Γ Ω 2 ( M ) . If R is a unital ℓ -ring, then each unital ℓ -module over...