Geodesic
On the Schröder-Bernstein problem for Carathéodory vector lattices
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 2, pp. 419-430.

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In this note we prove that there exists a Carathéodory vector lattice $V$ such that $V\cong V^3$ and $V\ncong V^2$. 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.
Classification : 06F15, 06F20, 46A40
Keywords: vecrot lattice; Boolean algebra; internal direct factor 
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     author = {Jakub{\'\i}k, J\'an},
     title = {On the {Schr\"oder-Bernstein} problem for {Carath\'eodory} vector lattices},
     journal = {Czechoslovak Mathematical Journal},
     pages = {419--430},
     publisher = {mathdoc},
     volume = {59},
     number = {2},
     year = {2009},
     mrnumber = {2532383},
     zbl = {1224.46006},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2009__59_2_a9/}
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Jakubík, Ján. On the Schröder-Bernstein problem for Carathéodory vector lattices. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 2, pp. 419-430. http://geodesic.mathdoc.fr/item/CMJ_2009__59_2_a9/