Published in Algebra and Logic
We give a characterization of complete strongly dually atomic lattices having unique irredundant decompositions which are also canonical. It is shown that all known characterizations of lattices with unique irredundant decompositions are a consequence of this result. In addition, upper continuous closure lattices of convex geometries with (unique) ...
A rational map with good reduction in the field $\mathbb{Q}_p$ of $p$-adic numbers defines a $1$-Lipschitz dynamical system on the projective line $\mathbb{P}^1(\mathbb{Q}_p)$ over $\mathbb{Q}_p$. The dynamical structure of such a system is completely described by a minimal decomposition. That is to say, $\mathbb{P}^1(\mathbb{Q}_p)$ is decomposed i...
Published in Letters in Mathematical Physics
The disjointness of measures and their Hahn–Jordan decomposition are instances of the general notion of minimal decomposition in base normed spaces. The mixing distance, a specification of a novel concept of angle in real normed vector spaces, is applied to provide a geometric interpretation of disjointness as orthogonality.
