Lattice separation, coseparation and regular measures.
Lattice uniformities on orthomodular structures
Logics with separating sets of measures
Lower semicontinuous functions with values in a continuous lattice
It is proved that for every continuous lattice there is a unique semiuniform structure generating both the order and the Lawson topology. The way below relation can be characterized with this uniform structure. These results are used to extend many of the analytical properties of real-valued l.s.cḟunctions to l.s.cḟunctions with values in a continuous lattice. The results of this paper have some applications in potential theory.
Metrics and tolerances
Metrizable completely distributive lattices
The purpose of this paper is to study the topological properties of the interval topology on a completely distributive lattice. The main result is that a metrizable completely distributive lattice is an ANR if and only if it contains at most finite completely compact elements.
Metrization of uniform lattices
Normal characterizations of lattices.
Normal lattices and coseparation of lattices.
On compactness of lattices.
On coverings in the lattice of all group topologies of arbitrary Abelian groups.
On Jónsson's theorem
A proof of Jonsson's theorem inspired by considering a natural topology on algebraic lattices is given.
On lattice-topological properties of general Wallman spaces.
On normal and strongly normal lattices.
On some notions related to compactness for locales
On the lattice of convexly compatible topologies on a partially ordered set
On topologies convexly compatible with the ordering
On valuation in semilattices
Order convergence and compactness
Orthomodular lattices and closure operations in ordered vector spaces
On a non-trivial partially ordered real vector space (V,≤) the orthogonality relation is defined by incomparability and ζ(V,⊥) is a complete lattice of double orthoclosed sets. We say that A ⊆ V is an orthogonal set when for all a,b ∈ A with a ≠ b, we have a ⊥ b. In our earlier papers we defined an integrally open ordered vector space and two closure operations A → D(A) and . It was proved that V is integrally open iff for every orthogonal set A ⊆ V. In this paper we generalize this result. We...