Almost orthogonality and Hausdorff interval  topologies of
atomic lattice effect algebras

J 2010

Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras

PASEKA, Jan; Zdenka RIEČANOVÁ a Wu JUNDE

Základní údaje

Originální název

Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras

Autoři

PASEKA, Jan; Zdenka RIEČANOVÁ a Wu JUNDE

Vydání

Kybernetika : The Journal of the Czech Society for Cybernetics and Informatics, Praha, Institute of Information Theory and Auto, 2010, 0023-5954

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Česká republika

Utajení

není předmětem státního či obchodního tajemství

Odkazy

Czech Digital Mathematics Library

Impakt faktor

Impact factor: 0.461

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/10:00050680

Organizační jednotka

Přírodovědecká fakulta

UT WoS

000287421300004

Klíčová slova anglicky

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

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 19. 4. 2012 11:57, prof. RNDr. Jan Paseka, CSc.

Anotace

V originále

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 circle plus-operation in the order and interval topologies on them.

Návaznosti

GA201/06/0664, projekt VaV

Název: Kategoriální metody teorie struktur

Investor: Grantová agentura ČR, Kategoriální metody teorie struktur

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; Zdenka RIEČANOVÁ a Wu JUNDE. Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras. Kybernetika : The Journal of the Czech Society for Cybernetics and Informatics. Praha: Institute of Information Theory and Auto, 2010, roč. 46, č. 6, s. 953-970. ISSN 0023-5954.

@article{979859,
   author = {Paseka, Jan and Riečanová, Zdenka and Junde, Wu},
   article_location = {Praha},
   article_number = {6},
   keywords = {non-classical logics; D-posets; effect algebras; MV-algebras; interval and order topology; states},
   language = {eng},
   issn = {0023-5954},
   journal = {Kybernetika : The Journal of the Czech Society for Cybernetics and Informatics},
   title = {Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras},
   url = {http://hdl.handle.net/10338.dmlcz/141459},
   volume = {46},
   year = {2010}
}

TY  - JOUR
ID  - 979859
AU  - Paseka, Jan - Riečanová, Zdenka - Junde, Wu
PY  - 2010
TI  - Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras
JF  - Kybernetika : The Journal of the Czech Society for Cybernetics and Informatics
VL  - 46
IS  - 6
SP  - 953-970
EP  - 953-970
PB  - Institute of Information Theory and Auto
SN  - 00235954
KW  - non-classical logics
KW  - D-posets
KW  - effect algebras
KW  - MV-algebras
KW  - interval and order topology
KW  - states
UR  - http://hdl.handle.net/10338.dmlcz/141459
L2  - http://hdl.handle.net/10338.dmlcz/141459
N2  - 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 circle plus-operation in the order and interval topologies on them.
ER  -

PASEKA, Jan; Zdenka RIEČANOVÁ a Wu JUNDE. Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras. \textit{Kybernetika : The Journal of the Czech Society for Cybernetics and Informatics}. Praha: Institute of Information Theory and Auto, 2010, roč.~46, č.~6, s.~953-970. ISSN~0023-5954.

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