Abstract
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.
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