| Title:
|
On the Schröder-Bernstein problem for Carathéodory vector lattices (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
419-430 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
vecrot lattice |
| Keyword:
|
Boolean algebra |
| Keyword:
|
internal direct factor |
| MSC:
|
06F15 |
| MSC:
|
06F20 |
| MSC:
|
46A40 |
| idZBL:
|
Zbl 1224.46006 |
| idMR:
|
MR2532383 |
| . |
| Date available:
|
2010-07-20T15:17:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140489 |
| . |
| Reference:
|
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| Reference:
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