Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras
| Authors | |
|---|---|
| Year of publication | 2010 |
| Type | Article in Periodical |
| Magazine / Source | Kybernetika : The Journal of the Czech Society for Cybernetics and Informatics |
| MU Faculty or unit | |
| Citation | |
| Web | Czech Digital Mathematics Library |
| Field | General mathematics |
| Keywords | non-classical logics; D-posets; effect algebras; MV-algebras; interval and order topology; states |
| 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 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. |
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