About: Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras     Goto   Sponge   Distinct   Permalink

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  • We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L Moreover, if L is complete then L is (o)-topological Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.
  • We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L Moreover, if L is complete then L is (o)-topological Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated. (en)
Title
  • Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
  • Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras (en)
skos:prefLabel
  • Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
  • Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras (en)
skos:notation
  • RIV/00216224:14310/10:00049168!RIV11-GA0-14310___
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  • P(GA201/06/0664)
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  • 12
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  • 251301
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  • RIV/00216224:14310/10:00049168
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  • ompact element; Compactly generated; de Morgan lattice; Basic algebra; Lattice effect algebra (en)
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  • US - Spojené státy americké
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  • [80DAF02118B4]
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  • International Journal of Theoretical Physics
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  • 49
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  • Paseka, Jan
  • Riečanová, Zdenka
http://linked.open...ain/vavai/riv/wos
  • 000284335300029
issn
  • 0020-7748
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  • 14310
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