On Carathéodory vector lattices

Ján Jakubík

Displaying similar documents to “On Carathéodory vector lattices”

Torsion classes and subdirect products of Carathéodory vector lattices

Ján Jakubík (2006)

Mathematica Slovaca

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On vector lattices of elementary Carathéodory functions

Ján Jakubík (2005)

Czechoslovak Mathematical Journal

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In this paper we deal with the vector lattice $C (B)$ of all elementary Carathéodory functions corresponding to a generalized Boolean algebra $B$ .

On the Schröder-Bernstein problem for Carathéodory vector lattices

Ján Jakubík (2009)

Czechoslovak Mathematical Journal

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In this note we prove that there exists a Carathéodory vector lattice $V$ such that $V ≅ V^{3}$ and $V ≇ V^{2}$ . This yields that $V$ is a solution of the Schröder-Bernstein problem for Carathéodory vector lattices. We also show that no Carathéodory Banach lattice is a solution of the Schröder-Bernstein problem.

Subdirect decompositions and the radical of a generalized Boolean algebra extension of a lattice ordered group

Ján Jakubík (2006)

Czechoslovak Mathematical Journal

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The extension of a lattice ordered group $A$ by a generalized Boolean algebra $B$ will be denoted by $A_{B}$ . In this paper we apply subdirect decompositions of $A_{B}$ for dealing with a question proposed by Conrad and Darnel. Further, in the case when $A$ is linearly ordered we investigate (i) the completely subdirect decompositions of $A_{B}$ and those of $B$ , and (ii) the values of elements of $A_{B}$ and the radical $R (A_{B})$ .

Cantor-Bernstein theorem for lattices

Ján Jakubík (2002)

Mathematica Bohemica

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This paper is a continuation of a previous author’s article; the result is now extended to the case when the lattice under consideration need not have the least element.