Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras

Investor logo

Warning

This publication doesn't include Faculty of Economics and Administration. It includes Faculty of Science. Official publication website can be found on muni.cz.
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:

You are running an old browser version. We recommend updating your browser to its latest version.