| Title:
|
Unique $a$-closure for some $\ell$-groups of rational valued functions (English) |
| Author:
|
Hager, Anthony W. |
| Author:
|
Kimber, Chawne M. |
| Author:
|
McGovern, Warren W. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
409-421 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Usually, an abelian $\ell $-group, even an archimedean $\ell $-group, has a relatively large infinity of distinct $a$-closures. Here, we find a reasonably large class with unique and perfectly describable $a$-closure, the class of archimedean $\ell $-groups with weak unit which are “$\mathbb Q$-convex”. ($\mathbb Q$ is the group of rationals.) Any $C(X,\mathbb Q)$ is $\mathbb Q$-convex and its unique $a$-closure is the Alexandroff algebra of functions on $X$ defined from the clopen sets; this is sometimes $C(X)$. (English) |
| Keyword:
|
archimedean lattice-ordered group |
| Keyword:
|
$a$-closure |
| Keyword:
|
rational-valued functions |
| Keyword:
|
zero-dimensional space |
| MSC:
|
06F20 |
| MSC:
|
06F25 |
| MSC:
|
20F60 |
| MSC:
|
54C30 |
| MSC:
|
54F65 |
| idZBL:
|
Zbl 1081.06020 |
| idMR:
|
MR2137147 |
| . |
| Date available:
|
2009-09-24T11:23:58Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127987 |
| . |
| Reference:
|
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