Frink ideal topology of lattice effect algebras

A difficult question arising in the study of effect algebras is how to equip them with a fitting and proper topology such that the topology is compatible with the partial operations ⊕ and Θ. As we know, the Frink ideal topology is an important intrinsic topology for studying partially ordered set th...

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Bibliographic Details
Published inReports on mathematical physics Vol. 61; no. 3; pp. 327 - 335
Main Authors Lei, Qiang, Wu, Junde, Li, Ronglu
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.06.2008
Subjects
continuity
effect algebras
Frink ideal topology
continuity
effect algebras
Frink ideal topology
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Summary:A difficult question arising in the study of effect algebras is how to equip them with a fitting and proper topology such that the topology is compatible with the partial operations ⊕ and Θ. As we know, the Frink ideal topology is an important intrinsic topology for studying partially ordered set theory; in particular, it is the correct topology for chains and direct products of a finite number of chains. In this paper, we show that the Frink ideal topology is also a nice topology for studying effect-algebra theory since it provides the operations with some of the expected continuity properties.
ISSN:0034-4877
1879-0674
DOI:10.1016/S0034-4877(08)00015-3