Orthomodular lattices with almost orthogonal sets of atoms

Pulmannová, Sylvia, and Rogalewicz, Vladimír. "Orthomodular lattices with almost orthogonal sets of atoms." Commentationes Mathematicae Universitatis Carolinae 32.3 (1991): 423-429. <http://eudml.org/doc/247290>.

@article{Pulmannová1991,
abstract = {The set $A$ of all atoms of an atomic orthomodular lattice is said to be almost orthogonal if the set $\lbrace b\in A:b\nleq a^\{\prime \}\rbrace $ is finite for every $a\in A$. It is said to be strongly almost orthogonal if, for every $a\in A$, any sequence $b_1, b_2,\dots $ of atoms such that $a\nleq b^\{\prime \}_1, b_1 \nleq b^\{\prime \}_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 orthogonal.},
author = {Pulmannová, Sylvia, Rogalewicz, Vladimír},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {atomic orthomodular lattice; topological orthomodular lattice; almost orthogonal sets of atoms; almost orthogonal sets of atoms; atomic orthomodular lattice; topological orthomodular lattices},
language = {eng},
number = {3},
pages = {423-429},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Orthomodular lattices with almost orthogonal sets of atoms},
url = {http://eudml.org/doc/247290},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Pulmannová, Sylvia
AU - Rogalewicz, Vladimír
TI - Orthomodular lattices with almost orthogonal sets of atoms
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 3
SP - 423
EP - 429
AB - The set $A$ of all atoms of an atomic orthomodular lattice is said to be almost orthogonal if the set $\lbrace b\in A:b\nleq a^{\prime }\rbrace $ is finite for every $a\in A$. It is said to be strongly almost orthogonal if, for every $a\in A$, any sequence $b_1, b_2,\dots $ of atoms such that $a\nleq b^{\prime }_1, b_1 \nleq b^{\prime }_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 orthogonal.
LA - eng
KW - atomic orthomodular lattice; topological orthomodular lattice; almost orthogonal sets of atoms; almost orthogonal sets of atoms; atomic orthomodular lattice; topological orthomodular lattices
UR - http://eudml.org/doc/247290
ER -