Almost orthogonality and Hausdorff interval topologies of atomic latice effect algebras

Title:

Almost orthogonality and Hausdorff interval topologies of atomic latice effect algebras

Creator:

Paseka, Jan, Riečanová, Zdenka, and Junde, Wu

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:1f9dc32e-6b69-4b0f-8276-6cd3eb55c329
uuid:1f9dc32e-6b69-4b0f-8276-6cd3eb55c329

Subject:

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

Type:

model:article and TEXT

Format:

bez média and svazek

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 ⊕-operation in the order and interval topologies on them.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[953]-970

Source:

Kybernetika | 2010 Volume:46 | Number:6

Harvested from:

CDK

Metadata only:

false