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On the Schröder-Bernstein problem for carathéodory vector lattices

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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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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, SK-040 01, Košice, Slovakia

    Ján Jakubík

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  1. Ján Jakubík
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Correspondence to Ján Jakubík.

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Supported by VEGA Agency grant 2/7141/27, by the Slovak Research and Development Agency under the contract No. APVV-0071-06, partially supported by the Slovak Academy of Sciences via the project Center of Excellence—Physics of Information, grant I/2/2005.

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Jakubík, J. On the Schröder-Bernstein problem for carathéodory vector lattices. Czech Math J 59, 419–430 (2009). https://doi.org/10.1007/s10587-009-0029-z

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  • DOI: https://doi.org/10.1007/s10587-009-0029-z

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