Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F10%3A00050680" target="_blank" >RIV/00216224:14310/10:00050680 - isvavai.cz</a>
Result on the web
<a href="http://hdl.handle.net/10338.dmlcz/141459" target="_blank" >http://hdl.handle.net/10338.dmlcz/141459</a>
DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras
Original language description
We prove that the interval topology of an Archimedean atomic lattice effect algebra E is Hausdorff whenever the set of all atoms of E is almost orthogonal. In such a case E is order continuous. If moreover E is complete then order convergence of nets ofelements of E is topological and hence it coincides with convergence in the order topology and this topology is compact Hausdorff compatible with a uniformity induced by a separating function family on E corresponding to compact and cocompact elements. For block-finite Archimedean atomic lattice effect algebras the equivalence of almost orthogonality and s-compact generation is shown. As the main application we obtain a state smearing theorem for these effect algebras, as well as the continuity of circle plus-operation in the order and interval topologies on them.
Czech name
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Czech description
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Classification
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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Result continuities
Project
<a href="/en/project/GA201%2F06%2F0664" target="_blank" >GA201/06/0664: Categorical methods of the theory of structures</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Kybernetika : The Journal of the Czech Society for Cybernetics and Informatics
ISSN
0023-5954
e-ISSN
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Volume of the periodical
46
Issue of the periodical within the volume
6
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
18
Pages from-to
953-970
UT code for WoS article
000287421300004
EID of the result in the Scopus database
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