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States, uniformities and metrics on lattice effect algebras. (English) Zbl 1059.03079

In the paper, various topologies on lattice-ordered effect algebras are studied. These are order and interval topologies, as well as uniform and pseudometric topologies induced by a state. In particular, several natural sufficient conditions are presented under which some, or all, of these topologies coincide or have a particular property, e.g., compactness.

MSC:

03G12 Quantum logic
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
06F30 Ordered topological structures
54D30 Compactness
54E45 Compact (locally compact) metric spaces
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