Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras

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Authors	PASEKA Jan RIEČANOVÁ Zdenka
Year of publication	2010
Type	Article in Periodical
Magazine / Source	International Journal of Theoretical Physics
MU Faculty or unit	Faculty of Science
Citation
web	http://www.springerlink.com/content/231n27j3p4108k86/
Field	General mathematics
Keywords	ompact element; Compactly generated; de Morgan lattice; Basic algebra; Lattice effect algebra
Description	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.
Related projects:	Kategoriální metody teorie struktur