| PASEKA, Jan a Zdenka RIEČANOVÁ. Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras. International Journal of Theoretical Physics. SPRINGER/PLENUM PUBLISHERS, 2010, roč. 49, č. 12, s. 3216-3223. ISSN 0020-7748. |
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@article{917418,
author = {Paseka, Jan and Riečanová, Zdenka},
article_number = {12},
keywords = {ompact element; Compactly generated; de Morgan lattice; Basic algebra; Lattice effect algebra},
language = {eng},
issn = {0020-7748},
journal = {International Journal of Theoretical Physics},
title = {Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras},
url = {http://www.springerlink.com/content/231n27j3p4108k86/},
volume = {49},
year = {2010}
}
TY - JOUR
ID - 917418
AU - Paseka, Jan - Riečanová, Zdenka
PY - 2010
TI - Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
JF - International Journal of Theoretical Physics
VL - 49
IS - 12
SP - 3216-3223
EP - 3216-3223
PB - SPRINGER/PLENUM PUBLISHERS
SN - 00207748
KW - ompact element
KW - Compactly generated
KW - de Morgan lattice
KW - Basic algebra
KW - Lattice effect algebra
UR - http://www.springerlink.com/content/231n27j3p4108k86/
N2 - 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.
ER -
PASEKA, Jan a Zdenka RIEČANOVÁ. Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras. \textit{International Journal of Theoretical Physics}. SPRINGER/PLENUM PUBLISHERS, 2010, roč.~49, č.~12, s.~3216-3223. ISSN~0020-7748.
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