| Title:
|
On locally solid topological lattice groups (English) |
| Author:
|
Khan, Abdul Rahim |
| Author:
|
Rowlands, Keith |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
963-973 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(G,\tau )$ be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If $(G,\tau )$ has the $A$(iii)-property, then its completion $(\widehat{G},\hat{\tau })$ is an order-complete locally solid lattice group. (2) If $G$ is order-complete and $\tau $ has the Fatou property, then the order intervals of $G$ are $\tau $-complete. (3) If $(G,\tau )$ has the Fatou property, then $G$ is order-dense in $\widehat{G}$ and $(\widehat{G},\hat{\tau })$ has the Fatou property. (4) The order-bound topology on any commutative lattice group is the finest locally solid topology on it. As an application, a version of the Nikodym boundedness theorem for set functions with values in a class of locally solid topological groups is established. (English) |
| Keyword:
|
topological completion |
| Keyword:
|
locally solid $\ell $-group |
| Keyword:
|
topological continuity |
| Keyword:
|
Fatou property |
| Keyword:
|
order-bound topology |
| MSC:
|
28B15 |
| MSC:
|
46A40 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 1174.54025 |
| idMR:
|
MR2356933 |
| . |
| Date available:
|
2009-09-24T11:50:55Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128219 |
| . |
| Reference:
|
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| . |
