J. Jakubik, Mathematical Institute, Slovak Academy of Sciences, Gresakova 6, SK-040 01 Kosice, Slovakia, e-mail: kstefan@saske.sk
Abstract: In this note we prove that there exists a Caratheodory vector lattice $V$ such that $V\cong V^3$ and $V\ncong V^2$. This yields that $V$ is a solution of the Schroder-Bernstein problem for Caratheodory vector lattices. We also show that no Caratheodory Banach lattice is a solution of the Schroder-Bernstein problem.
Keywords: vecrot lattice, Boolean algebra, internal direct factor
Classification (MSC 2000): 46A40, 06F20, 06F15
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