| Title:
|
Locally solid topological lattice-ordered groups (English) |
| Author:
|
Hong, Liang |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
107-128 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper is an attempt to initiate a relatively systematic study of locally solid topological lattice-ordered groups. We give both Roberts-Namioka-type characterization and Fremlin-type characterization of locally solid topological lattice-ordered groups. In particular, we show that a group topology on a lattice-ordered group is locally solid if and only if it is generated by a family of translation-invariant lattice pseudometrics. We also investigate (1) the basic properties of lattice group homomorphism on locally solid topological lattice-ordered groups; (2) the relationship between order-bounded subsets and topologically bounded subsets in locally solid topological lattice-ordered groups; (3) the Hausdorff completion of locally solid topological lattice-ordered groups. (English) |
| Keyword:
|
characterization |
| Keyword:
|
Hausdorff completion |
| Keyword:
|
lattice homomorphisms |
| Keyword:
|
locally solid topological $l$-groups |
| Keyword:
|
neighborhood theorem |
| Keyword:
|
order-bounded subsets |
| MSC:
|
06B35 |
| MSC:
|
06F15 |
| MSC:
|
06F20 |
| MSC:
|
06F30 |
| MSC:
|
20F60 |
| MSC:
|
22A26 |
| idZBL:
|
Zbl 06487024 |
| idMR:
|
MR3367096 |
| DOI:
|
10.5817/AM2015-2-107 |
| . |
| Date available:
|
2015-06-24T13:42:47Z |
| Last updated:
|
2016-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144310 |
| . |
| Reference:
|
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