Geodesic
Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras
Kybernetika, Tome 46 (2010) no. 6, pp. 953-970 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $øplus$-operation in the order and interval topologies on them.
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 $øplus$-operation in the order and interval topologies on them.
Classification : 03G12, 03G25, 06F05, 08A55, 54H12
Keywords: non-classical logics; D-posets; effect algebras; $MV$-algebras; interval and order topology; states 
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Paseka, Jan; Riečanová, Zdenka; Wu, Junde. Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras. Kybernetika, Tome 46 (2010) no. 6, pp. 953-970. http://geodesic.mathdoc.fr/item/KYB_2010_46_6_a3/

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