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

J 2013

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

PASEKA, Jan, Wu JUNDE a Lei QIANG

Základní údaje

Originální název

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

Autoři

PASEKA, Jan (203 Česká republika, garant, domácí), Wu JUNDE (156 Čína) a Lei QIANG (156 Čína)

Vydání

International Journal of Theoretical Physics, Springer, 2013, 0020-7748

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.186

Kód RIV

RIV/00216224:14310/13:00070762

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1007/s10773-012-1465-3

UT WoS

000318373700034

Klíčová slova anglicky

Interval and order topology; De Morgan lattice; Effect algebra; Compact element; Hypercompact element

Štítky

AKR, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 3. 1. 2014 18:14, prof. RNDr. Jan Paseka, CSc.

Anotace

V originále

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 interval topology 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.

Návaznosti

EE2.3.20.0051, projekt VaV

Název: Algebraické metody v kvantové logice

MSM0021622409, záměr

Název: Matematické struktury a jejich fyzikální aplikace

Investor: Ministerstvo školství, mládeže a tělovýchovy ČR, Matematické struktury a jejich fyzikální aplikace

Citovat

PASEKA, Jan, Wu JUNDE a Lei QIANG. Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras. International Journal of Theoretical Physics. Springer, 2013, roč. 52, č. 6, s. 2055-2064. ISSN 0020-7748. Dostupné z: https://dx.doi.org/10.1007/s10773-012-1465-3.

@article{1138661,
   author = {Paseka, Jan and Junde, Wu and Qiang, Lei},
   article_number = {6},
   doi = {http://dx.doi.org/10.1007/s10773-012-1465-3},
   keywords = {Interval and order topology; De Morgan lattice; Effect algebra; Compact element; Hypercompact element},
   language = {eng},
   issn = {0020-7748},
   journal = {International Journal of Theoretical Physics},
   title = {Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras},
   url = {http://link.springer.com/article/10.1007/s10773-012-1465-3},
   volume = {52},
   year = {2013}
}

TY  - JOUR
ID  - 1138661
AU  - Paseka, Jan - Junde, Wu - Qiang, Lei
PY  - 2013
TI  - Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras
JF  - International Journal of Theoretical Physics
VL  - 52
IS  - 6
SP  - 2055-2064
EP  - 2055-2064
PB  - Springer
SN  - 00207748
KW  - Interval and order topology
KW  - De Morgan lattice
KW  - Effect algebra
KW  - Compact element
KW  - Hypercompact element
UR  - http://link.springer.com/article/10.1007/s10773-012-1465-3
L2  - http://link.springer.com/article/10.1007/s10773-012-1465-3
N2  - 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 interval topology 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.
ER  -

PASEKA, Jan, Wu JUNDE a Lei QIANG. Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras. \textit{International Journal of Theoretical Physics}. Springer, 2013, roč.~52, č.~6, s.~2055-2064. ISSN~0020-7748. Dostupné z: https://dx.doi.org/10.1007/s10773-012-1465-3.

Podrobný výpis o publikaci