About: Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras     Goto   Sponge   NotDistinct   Permalink

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Description
  • 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.
  • 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. (en)
Title
  • Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras
  • Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras (en)
skos:prefLabel
  • Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras
  • Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras (en)
skos:notation
  • RIV/00216224:14310/13:00070762!RIV14-MSM-14310___
http://linked.open...avai/riv/aktivita
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  • P(EE2.3.20.0051), Z(MSM0021622409)
http://linked.open...iv/cisloPeriodika
  • 6
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  • 60138
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  • RIV/00216224:14310/13:00070762
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  • Interval and order topology; De Morgan lattice; Effect algebra; Compact element; Hypercompact element (en)
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  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [338B8F2DD529]
http://linked.open...i/riv/nazevZdroje
  • International Journal of Theoretical Physics
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  • 52
http://linked.open...iv/tvurceVysledku
  • Paseka, Jan
  • Junde, Wu
  • Qiang, Lei
http://linked.open...ain/vavai/riv/wos
  • 000318373700034
http://linked.open...n/vavai/riv/zamer
issn
  • 0020-7748
number of pages
http://bibframe.org/vocab/doi
  • 10.1007/s10773-012-1465-3
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  • 14310
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