Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F13%3A00070762" target="_blank" >RIV/00216224:14310/13:00070762 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/article/10.1007/s10773-012-1465-3" target="_blank" >http://link.springer.com/article/10.1007/s10773-012-1465-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-012-1465-3" target="_blank" >10.1007/s10773-012-1465-3</a>

Result language
angličtina
Original language name
Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras
Original language description
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 intervaltopology 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/EE2.3.20.0051" target="_blank" >EE2.3.20.0051: Algebraic methods in Quantum Logic</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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