On the Schröder-Bernstein problem for Carathéodory vector lattices

Ján Jakubík

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 2, page 419-430
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Jakubík, Ján. "On the Schröder-Bernstein problem for Carathéodory vector lattices." Czechoslovak Mathematical Journal 59.2 (2009): 419-430. <http://eudml.org/doc/37932>.

@article{Jakubík2009,
abstract = {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.},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {vecrot lattice; Boolean algebra; internal direct factor; vector lattice; Boolean algebra; internal direct factor},
language = {eng},
number = {2},
pages = {419-430},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Schröder-Bernstein problem for Carathéodory vector lattices},
url = {http://eudml.org/doc/37932},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Jakubík, Ján
TI - On the Schröder-Bernstein problem for Carathéodory vector lattices
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 419
EP - 430
AB - 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.
LA - eng
KW - vecrot lattice; Boolean algebra; internal direct factor; vector lattice; Boolean algebra; internal direct factor
UR - http://eudml.org/doc/37932
ER -

References

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