| Title:
|
Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras (English) |
| Author:
|
Paseka, Jan |
| Author:
|
Riečanová, Zdenka |
| Author:
|
Wu, Junde |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
46 |
| Issue:
|
6 |
| Year:
|
2010 |
| Pages:
|
953-970 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that the interval topology of an Archimedean atomic lattice effect algebra $E$ is Hausdorff whenever the set of all atoms of $E$ is almost orthogonal. In such a case $E$ is order continuous. If moreover $E$ is complete then order convergence of nets of elements of $E$ is topological and hence it coincides with convergence in the order topology and this topology is compact Hausdorff compatible with a uniformity induced by a separating function family on $E$ corresponding to compact and cocompact elements. For block-finite Archimedean atomic lattice effect algebras the equivalence of almost orthogonality and s-compact generation is shown. As the main application we obtain a state smearing theorem for these effect algebras, as well as the continuity of $øplus$-operation in the order and interval topologies on them. (English) |
| Keyword:
|
non-classical logics |
| Keyword:
|
D-posets |
| Keyword:
|
effect algebras |
| Keyword:
|
$MV$-algebras |
| Keyword:
|
interval and order topology |
| Keyword:
|
states |
| MSC:
|
03G12 |
| MSC:
|
03G25 |
| MSC:
|
06F05 |
| MSC:
|
08A55 |
| MSC:
|
54H12 |
| idZBL:
|
Zbl 1229.03055 |
| idMR:
|
MR2797420 |
| . |
| Date available:
|
2011-04-12T12:43:02Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141459 |
| . |
| Reference:
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