| PASEKA, Jan, Zdenka RIEČANOVÁ a Wu JUNDE. Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras. Online. Kybernetika : The Journal of the Czech Society for Cybernetics and Informatics. Praha: Institute of Information Theory and Auto, 2010, roč. 46, č. 6, s. 953-970. ISSN 0023-5954. [citováno 2024-04-24] |
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@article{979859,
author = {Paseka, Jan and Riečanová, Zdenka and Junde, Wu},
article_location = {Praha},
article_number = {6},
keywords = {non-classical logics; D-posets; effect algebras; MV-algebras; interval and order topology; states},
language = {eng},
issn = {0023-5954},
journal = {Kybernetika : The Journal of the Czech Society for Cybernetics and Informatics},
title = {Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras},
url = {http://hdl.handle.net/10338.dmlcz/141459},
volume = {46},
year = {2010}
}
TY - JOUR
ID - 979859
AU - Paseka, Jan - Riečanová, Zdenka - Junde, Wu
PY - 2010
TI - Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras
JF - Kybernetika : The Journal of the Czech Society for Cybernetics and Informatics
VL - 46
IS - 6
SP - 953-970
EP - 953-970
PB - Institute of Information Theory and Auto
SN - 00235954
KW - non-classical logics
KW - D-posets
KW - effect algebras
KW - MV-algebras
KW - interval and order topology
KW - states
UR - http://hdl.handle.net/10338.dmlcz/141459
L2 - http://hdl.handle.net/10338.dmlcz/141459
N2 - 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 of elements 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.
ER -
PASEKA, Jan, Zdenka RIEČANOVÁ a Wu JUNDE. Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras. Online. \textit{Kybernetika : The Journal of the Czech Society for Cybernetics and Informatics}. Praha: Institute of Information Theory and Auto, 2010, roč.~46, č.~6, s.~953-970. ISSN~0023-5954. [citováno 2024-04-24]
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