ALMOST ORTHOGONALITY AND HAUSDORFF INTERVAL TOPOLOGIES OF ATOMIC LATTICE EFFECT ALGEBRAS

作者：Paseka Jan^*; Riecanova Zdenka; Wu Junde

来源：Kybernetika, 2010, 46(6): 953-970.

• non-classical logics
• D-posets
• effect algebras
• MV-algebras
• interval and order topology
• states

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.

• 出版日期2010
• 单位浙江大学