The lattices of topologies on a partially ordered set
The new interval topology on lattice products
The spectral theory of semitopological semilattices.
The Tensor Product of Continuous Lattices.
Tietze's convexity theorey for lattices and semilattices.
Topological characterization of certain classes of lattices
Topological difference posets
Topological properties of generalized Wallman spaces and lattice relations.
Topologies generated by ideals
A topological space is said to be generated by an ideal if for all and all there is in such that , and is said to be weakly generated by if whenever a subset of contains for every with , then itself is closed. An important class of examples are the so called weakly discretely generated spaces (which include sequential, scattered and compact Hausdorff spaces). Another paradigmatic example is the class of Alexandroff spaces which corresponds to spaces generated by finite sets....
Two extension theorems. Modular functions on complemented lattices
We prove an extension theorem for modular functions on arbitrary lattices and an extension theorem for measures on orthomodular lattices. The first is used to obtain a representation of modular vector-valued functions defined on complemented lattices by measures on Boolean algebras. With the aid of this representation theorem we transfer control measure theorems, Vitali-Hahn-Saks and Nikodým theorems and the Liapunoff theorem about the range of measures to the setting of modular functions on complemented...