×

Complemented uniform lattices. (English) Zbl 1121.54312

Summary: It is proved that the completion of a complemented modular lattice with respect to a Hausdorff lattice uniformity which is metrizable or exhaustive is a complemented modular lattice. It is then shown that a complete complemented modular lattice endowed with a Hausdorff order continuous lattice uniformity is isomorphic to the product of an arcwise connected complemented lattice and of geometric lattices of finite length each of which endowed with the discrete uniformity. These two results are used to prove a decomposition theorem for modular functions on complemented lattices.

MSC:

54H13 Topological fields, rings, etc. (topological aspects)
06B30 Topological lattices
06C20 Complemented modular lattices, continuous geometries
54E15 Uniform structures and generalizations
PDFBibTeX XMLCite
Full Text: DOI