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The $α$ -completion of a lattice ordered group

Richard N. Ball, Gary Davis (1983)

Czechoslovak Mathematical Journal

The $σ$ -property in $C (X)$

Anthony W. Hager (2016)

Commentationes Mathematicae Universitatis Carolinae

The $σ$ -property of a Riesz space (real vector lattice) $B$ is: For each sequence ${b_{n}}$ of positive elements of $B$ , there is a sequence ${λ_{n}}$ of positive reals, and $b \in B$ , with $λ_{n} b_{n} \leq b$ for each $n$ . This condition is involved in studies in Riesz spaces of abstract Egoroff-type theorems, and of the countable lifting property. Here, we examine when “ $σ$ ” obtains for a Riesz space of continuous real-valued functions $C (X)$ . A basic result is: For discrete $X$ , $C (X)$ has $σ$ iff the cardinal $| X | < 𝔟$ , Rothberger’s bounding number. Consequences and...

The σ-complete MV-algebras which have enough states

Antonio Di Nola, Mirko Navara (2005)

Colloquium Mathematicae

We characterize Łukasiewicz tribes, i.e., collections of fuzzy sets that are closed under the standard fuzzy complementation and the Łukasiewicz t-norm with countably many arguments. As a tool, we introduce σ-McNaughton functions as the closure of McNaughton functions under countable MV-algebraic operations. We give a measure-theoretical characterization of σ-complete MV-algebras which are isomorphic to Łukasiewicz tribes.

Théorie axiomatique de l'essentialité

Jacques Ravel (1967/1968)

Séminaire Dubreil. Algèbre et théorie des nombres

Théories de torsion et f-modules

Alain Bigard (1972/1973)

Séminaire Dubreil. Algèbre et théorie des nombres

Three generators for minimal writing-space computations

Serge Burckel, Marianne Morillon (2000)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Three generators for minimal writing-space computations

Serge Burckel, Marianne Morillon (2010)

RAIRO - Theoretical Informatics and Applications

We construct, for each integer n, three functions from {0,1}n to {0,1} such that any boolean mapping from {0,1}n to {0,1}n can be computed with a finite sequence of assignations only using the n input variables and those three functions.