Outer measure analysis of topological lattice properties.
Outer measures and associated lattice properties.
Partially-additive monoids
Polarity compatible with a closure system
Quasicontinuous spaces
We lift the notion of quasicontinuous posets to the topology context, called quasicontinuous spaces, and further study such spaces. The main results are: (1) A space is a quasicontinuous space if and only if is locally hypercompact if and only if is a hypercontinuous lattice; (2) a space is an -continuous space if and only if is a meet continuous and quasicontinuous space; (3) if a -space is a well-filtered poset under its specialization order, then is a quasicontinuous space...
Realcompactification and repleteness of Wallman spaces.
Remarks on the sobriety of Scott topology and weak topology on posets
We give some necessary and sufficient conditions for the Scott topology on a complete lattice to be sober, and a sufficient condition for the weak topology on a poset to be sober. These generalize the corresponding results in [1], [2] and [4].
Sequential convergences in distributive lattices
In this paper we investigate the system Conv of all sequential convergences on a distributive lattice .
Sequential convergences in lattices
The notion of sequential convergence on a lattice is defined in a natural way. In the present paper we investigate the system of all sequential convergences on a lattice .
Some properties of an ordering relation on certain classes of functors
Special measures and repleteness.
Sublattices of topologically represented lattices.
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.