Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F13%3A00070762" target="_blank" >RIV/00216224:14310/13:00070762 - isvavai.cz</a>

Výsledek na webu

<a href="http://link.springer.com/article/10.1007/s10773-012-1465-3" target="_blank" >http://link.springer.com/article/10.1007/s10773-012-1465-3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10773-012-1465-3" target="_blank" >10.1007/s10773-012-1465-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras

Popis výsledku v původním jazyce

The topologies on ordered structures have been intensively studied by mathematicians and computer scientists. Various types of topologies may be introduced, depending on the nature of the ordered sets considered. Our purpose here is to study the intervaltopology tau_i , the order topology tau_o and the topology tau_phi induced by a canonical intrinsic uniformity generated by a certain family of pseudometrics on de Morgan lattices. This uniformity and topology may be regarded as a ?two-sided symmetrization? of a similar intrinsic uniformity introduced by Erné and Palko for an order-theoretical construction of certain uniform completions. We prove that on a de Morgan lattice L with a join-dense set U the interval topology tau_i is Hausdorff and L is compactly generated by the elements of U if and only if L is U-almost orthogonal if and only if any element of U is hypercompact.

Název v anglickém jazyce

Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras

Popis výsledku anglicky

The topologies on ordered structures have been intensively studied by mathematicians and computer scientists. Various types of topologies may be introduced, depending on the nature of the ordered sets considered. Our purpose here is to study the intervaltopology tau_i , the order topology tau_o and the topology tau_phi induced by a canonical intrinsic uniformity generated by a certain family of pseudometrics on de Morgan lattices. This uniformity and topology may be regarded as a ?two-sided symmetrization? of a similar intrinsic uniformity introduced by Erné and Palko for an order-theoretical construction of certain uniform completions. We prove that on a de Morgan lattice L with a join-dense set U the interval topology tau_i is Hausdorff and L is compactly generated by the elements of U if and only if L is U-almost orthogonal if and only if any element of U is hypercompact.

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/EE2.3.20.0051" target="_blank" >EE2.3.20.0051: Algebraické metody v kvantové logice</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

2013

Kód důvěrnosti údajů

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

Název periodika

International Journal of Theoretical Physics

ISSN

0020-7748

e-ISSN

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Svazek periodika

52

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

2055-2064

Kód UT WoS článku

000318373700034

EID výsledku v databázi Scopus

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