Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F10%3A00050680" target="_blank" >RIV/00216224:14310/10:00050680 - isvavai.cz</a>

Výsledek na webu

<a href="http://hdl.handle.net/10338.dmlcz/141459" target="_blank" >http://hdl.handle.net/10338.dmlcz/141459</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras

Popis výsledku v původním jazyce

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 ofelements 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.

Název v anglickém jazyce

Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras

Popis výsledku anglicky

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 ofelements 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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F06%2F0664" target="_blank" >GA201/06/0664: Kategoriální metody teorie struktur</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2010

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Kybernetika : The Journal of the Czech Society for Cybernetics and Informatics

ISSN

0023-5954

e-ISSN

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Svazek periodika

46

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

18

Strana od-do

953-970

Kód UT WoS článku

000287421300004

EID výsledku v databázi Scopus

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