| Title:
|
Orthomodular lattices with almost orthogonal sets of atoms (English) |
| Author:
|
Pulmannová, Sylvia |
| Author:
|
Rogalewicz, Vladimír |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
3 |
| Year:
|
1991 |
| Pages:
|
423-429 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The set $A$ of all atoms of an atomic orthomodular lattice is said to be almost ortho\-go\-nal if the set $\{b\in A:b\nleq a'\}$ is finite for every $a\in A$. It is said to be strongly almost ortho\-go\-nal if, for every $a\in A$, any sequence $b_1, b_2,\dots $ of atoms such that $a\nleq b'_1, b_1 \nleq b'_2, \dots $ contains at most finitely many distinct elements. We study the relation and consequences of these notions. We show among others that a complete atomic orthomodular lattice is a compact topological one if and only if the set of all its atoms is almost ortho\-go\-nal. (English) |
| Keyword:
|
atomic orthomodular lattice |
| Keyword:
|
topological orthomodular lattice |
| Keyword:
|
almost orthogonal sets of atoms |
| MSC:
|
03G12 |
| MSC:
|
06C15 |
| idZBL:
|
Zbl 0762.06003 |
| idMR:
|
MR1159789 |
| . |
| Date available:
|
2009-01-08T17:45:45Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118422 |
| . |
| Reference:
|
[1] Chevalier G.: Around the relative center property in orthomodular lattices.preprint, 1989. Zbl 0795.06010, MR 1055767 |
| Reference:
|
[2] Janowitz M.: Separation conditions in relatively complemented lattices.Colloq. Math. 22 (1970), 25-34. Zbl 0209.03902, MR 0280419 |
| Reference:
|
[3] Kalmbach G.: Orthomodular Lattices.Academic Press, London, 1983. Zbl 0554.06009, MR 0716496 |
| Reference:
|
[4] Navara M., Rogalewicz V.: The pasting constructions for orthomodular posets.to appear in Math. Nachrichten. Zbl 0767.06009, MR 1138377 |
| Reference:
|
[5] Pulmannová S., Riečanová Z.: Compact topological orthomodular lattices.preprint, 1990. MR 1143091 |
| Reference:
|
[6] Tae Ho Choe, Greechie R.: Profinite orthomodular lattices.preprint. MR 1143016 |
| . |
