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

Varování

Publikace nespadá pod Filozofickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
Autoři

PASEKA Jan JUNDE Wu QIANG Lei

Rok publikování 2013
Druh Článek v odborném periodiku
Časopis / Zdroj International Journal of Theoretical Physics
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www http://link.springer.com/article/10.1007/s10773-012-1465-3
Doi http://dx.doi.org/10.1007/s10773-012-1465-3
Obor Obecná matematika
Klíčová slova Interval and order topology; De Morgan lattice; Effect algebra; Compact element; Hypercompact element
Popis 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.
Související projekty:

Používáte starou verzi internetového prohlížeče. Doporučujeme aktualizovat Váš prohlížeč na nejnovější verzi.