Distributivity for Upper Continuous and Strongly Atomic Lattices

An Analogue of Distributivity for Ungraded Lattices

In this paper, we define a property, trimness, for lattices. Trimness is a not-necessarily-graded generalization of distributivity; in particular, if a lattice is trim and graded, it is distributive. Trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sph...

From strongly interacting atomic systems to optical lattices

For more than a decade, cold atoms represented weakly interacting systems. Laser cooling achieved temperatures typically around 100 μK in a classical gas, far away from quantum degeneracy. Evaporative cooling led to Bose-Einstein condensation at temperatures typically around 100 nK. Bose-Einstein condensates are weakly interacting many-body systems described by mean field physics through the Gr...

Distributivity in lattices of fuzzy subgroups

The main goal of this paper is to study the finite groups whose lattices of fuzzy subgroups are distributive. We obtain a characterization of these groups which is similar to a wellknown result of group theory. 2008 Elsevier Inc. All rights reserved.

Measürability and Distributivity in the Theory of Lattices

Weak Distributivity implying Distributivity

Let B be a complete Boolean algebra. We show that if λ is an infinite cardinal and B is weakly (λ, ω)-distributive, then B is (λ, 2)-distributive. Using a similar argument, we show that if κ is a weakly compact cardinal such that B is weakly (2, κ)distributive and B is (α, 2)-distributive for each α < κ, then B is (κ, 2)-distributive.