The duality between lattice-ordered monoids and ordered topological spaces.
The graphs of join-semilattices and the shape of congruence lattices of particle lattices
We attach to each -semilattice a graph whose vertices are join-irreducible elements of and whose edges correspond to the reflexive dependency relation. We study properties of the graph both when is a join-semilattice and when it is a lattice. We call a -semilattice particle provided that the set of its join-irreducible elements satisfies DCC and join-generates . We prove that the congruence lattice of a particle lattice is anti-isomorphic to the lattice of all hereditary subsets of...
The group of divisibility of
The ideal and new interval topologies on l-groups
The order topology for a von Neumann algebra
The order topology (resp. the sequential order topology ) on a poset P is the topology that has as its closed sets those that contain the order limits of all their order convergent nets (resp. sequences). For a von Neumann algebra M we consider the following three posets: the self-adjoint part , the self-adjoint part of the unit ball , and the projection lattice P(M). We study the order topology (and the corresponding sequential variant) on these posets, compare the order topology to the other...
The Redfield topology on some groups of continuous functions.
The Redfield topology on the space of real-valued continuous functions on a topological space is studied (we call it R-topology for short). The R-neighbourhoods are described relating them to the connectedness for the carriers. The main results are: If the space is totally disconnected without isolated points, the R-topology is not discrete. Under suitable conditions on the space, R-convergence implies pointwise or uniform convergence. Under some restrictions, R-convergence for a net implies that...
The spectral theory of semitopological semilattices.
The topology of continuous partially-additive monoids
Topological groups of divisibility
Topological properties of spaces ordered by preferences.
Topologies compatible with order and separation axioms
Topologies compatible with ordering
Topologies corresponding to metrics on -groups
Topology and axioms of interpolation in partially ordered spaces.
T-topologies on a lattice ordered group.
In this paper a characterization of the topologies on a l-group arising from a CTRO (T-topologies) is given. We use it to find conditions under which the Redfield topology comes from a CTRO.