| PASEKA, Jan, Wu JUNDE a Lei QIANG. Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras. International Journal of Theoretical Physics. Springer, 2013, roč. 52, č. 6, s. 2055-2064. ISSN 0020-7748. Dostupné z: https://dx.doi.org/10.1007/s10773-012-1465-3. |
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@article{1138661,
author = {Paseka, Jan and Junde, Wu and Qiang, Lei},
article_number = {6},
doi = {http://dx.doi.org/10.1007/s10773-012-1465-3},
keywords = {Interval and order topology; De Morgan lattice; Effect algebra; Compact element; Hypercompact element},
language = {eng},
issn = {0020-7748},
journal = {International Journal of Theoretical Physics},
title = {Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras},
url = {http://link.springer.com/article/10.1007/s10773-012-1465-3},
volume = {52},
year = {2013}
}
TY - JOUR
ID - 1138661
AU - Paseka, Jan - Junde, Wu - Qiang, Lei
PY - 2013
TI - Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras
JF - International Journal of Theoretical Physics
VL - 52
IS - 6
SP - 2055-2064
EP - 2055-2064
PB - Springer
SN - 00207748
KW - Interval and order topology
KW - De Morgan lattice
KW - Effect algebra
KW - Compact element
KW - Hypercompact element
UR - http://link.springer.com/article/10.1007/s10773-012-1465-3
L2 - http://link.springer.com/article/10.1007/s10773-012-1465-3
N2 - The topologies on ordered structures have been intensively studied by mathematicians and computer scientists. Various types of topologies may be introduced, depending on the nature of the ordered sets considered. Our purpose here is to study the interval topology tau_i , the order topology tau_o and the topology tau_phi induced by a canonical intrinsic uniformity generated by a certain family of pseudometrics on de Morgan lattices. This uniformity and topology may be regarded as a “two-sided symmetrization” of a similar intrinsic uniformity introduced by Erné and Palko for an order-theoretical construction of certain uniform completions. We prove that on a de Morgan lattice L with a join-dense set U the interval topology tau_i is Hausdorff and L is compactly generated by the elements of U if and only if L is U-almost orthogonal if and only if any element of U is hypercompact.
ER -
PASEKA, Jan, Wu JUNDE a Lei QIANG. Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras. \textit{International Journal of Theoretical Physics}. Springer, 2013, roč.~52, č.~6, s.~2055-2064. ISSN~0020-7748. Dostupné z: https://dx.doi.org/10.1007/s10773-012-1465-3.
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