Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 215-227 |
| Seitenumfang | 13 |
| Fachzeitschrift | Topology and its applications |
| Jahrgang | 61 |
| Ausgabenummer | 3 |
| Publikationsstatus | Veröffentlicht - 24 Feb. 1995 |
Abstract
A lattice is order-topological iff its order convergence is topological and makes the lattice operations continuous. We show that the following properties are equivalent for any complete orthomodular lattice L: 1. (i) L is order-topological, 2. (ii) L is continuous (in the sense of Scott), 3. (iii) L is algebraic, 4. (iv) L is compactly atomistic, 5. (v) L is a totally order-disconnected topological lattice in the order topology. A special class of complete order-topological orthomodular lattices, namely the compact topological orthomodular lattices, are characterized by various algebraic conditions, for example, by the existence of a join-dense subset of so-called hypercompact elements.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Geometrie und Topologie
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in: Topology and its applications, Jahrgang 61, Nr. 3, 24.02.1995, S. 215-227.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Order-topological complete orthomodular lattices
AU - Erné, Marcel
AU - Riečanová, Zdenka
PY - 1995/2/24
Y1 - 1995/2/24
N2 - A lattice is order-topological iff its order convergence is topological and makes the lattice operations continuous. We show that the following properties are equivalent for any complete orthomodular lattice L: 1. (i) L is order-topological, 2. (ii) L is continuous (in the sense of Scott), 3. (iii) L is algebraic, 4. (iv) L is compactly atomistic, 5. (v) L is a totally order-disconnected topological lattice in the order topology. A special class of complete order-topological orthomodular lattices, namely the compact topological orthomodular lattices, are characterized by various algebraic conditions, for example, by the existence of a join-dense subset of so-called hypercompact elements.
AB - A lattice is order-topological iff its order convergence is topological and makes the lattice operations continuous. We show that the following properties are equivalent for any complete orthomodular lattice L: 1. (i) L is order-topological, 2. (ii) L is continuous (in the sense of Scott), 3. (iii) L is algebraic, 4. (iv) L is compactly atomistic, 5. (v) L is a totally order-disconnected topological lattice in the order topology. A special class of complete order-topological orthomodular lattices, namely the compact topological orthomodular lattices, are characterized by various algebraic conditions, for example, by the existence of a join-dense subset of so-called hypercompact elements.
KW - Atomistic
KW - Compact
KW - Compactly generated
KW - Continuous
KW - Order convergence
KW - Order topology
KW - Order-topological
KW - Ortho(modular) lattice
KW - Totally order-disconnected
UR - http://www.scopus.com/inward/record.url?scp=0013153199&partnerID=8YFLogxK
U2 - 10.1016/0166-8641(94)00040-A
DO - 10.1016/0166-8641(94)00040-A
M3 - Article
AN - SCOPUS:0013153199
VL - 61
SP - 215
EP - 227
JO - Topology and its applications
JF - Topology and its applications
SN - 0166-8641
IS - 3
ER -