Lattice uniformities and modular functions on orthomodular lattices

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1995 Italy English Publisher:Springer Science and Business Media LLCJournal:Order, volume 12, pages 295-305 (issn: 0167-8094, eissn: 1572-9273,

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Authors: WEBER, Hans Josef Karl;

doi: 10.1007/bf01111744

handle: 11390/674694

Lattice uniformities and modular functions on orthomodular lattices

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Abstract

Traynor's decomposition for group-valued set functions is generalized to exhaustive modular functions. It is shown that the lattice of exhaustive (lattice-) uniformities on an orthomodular lattice \(L\) is a complete Boolean algebra isomorphic to the centre of a quotient completion of \(L\).

Country

Italy

Related Organizations

University of Udine
Italy

Keywords

Complemented lattices, orthocomplemented lattices and posets, decomposition, exhaustive modular functions, complete Boolean algebra, Ordered topological structures, orthomodular lattice, quotient completion, lattice of exhaustive uniformities, centre

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