On the equivalence of certain coincidence theorems and fixed point theorems
On the lattice of convexly compatible topologies on a partially ordered set
On the Nachbin compactification of products of totally ordered spaces.
On topologies convexly compatible with the ordering
On treelike neighbourhood spaces
On treelike proximity spaces
Open images of orderable spaces
Order compatibility for Cauchy spaces and convergence spaces.
Order extension of order monomorphisms on a preordered topological space.
Orderability form selections: Another solution to the orderability problem
Orderability of topological spaces by continuous preferences.
Ordered Cauchy spaces.
Ordered compactification of totally ordered spaces.
Ordered compactifications and families of maps.
Ordered spaces and quasi-uniformities on spaces of continuous order-preserving functions.
In this paper we introduce and investigate the notions of point open order topology, compact open order topology, the order topology of quasi-uniform pointwise convergence and the order topology of quasi-uniform convergence on compacta. We consider the functorial correspondence between function spaces in the categories of topological spaces, bitopological spaces and ordered topological spaces. We obtain extensions to the topological ordered case of classical topological results on function spaces....
Ordered spaces with special bases
We study the roles played by four special types of bases (weakly uniform bases, ω-in-ω bases, open-in-finite bases, and sharp bases) in the classes of linearly ordered and generalized ordered spaces. For example, we show that a generalized ordered space has a weakly uniform base if and only if it is quasi-developable and has a -diagonal, that a linearly ordered space has a point-countable base if and only if it is first-countable and has an ω-in-ω base, and that metrizability in a generalized ordered...
Ordered topological spaces and the coproduct of bounded distributive lattices
Order-like structure of monotonically normal spaces
For a compact monotonically normal space X we prove: (1) has a dense set of points with a well-ordered neighborhood base (and so is co-absolute with a compact orderable space); (2) each point of has a well-ordered neighborhood -base (answering a question of Arhangel’skii); (3) is hereditarily paracompact iff has countable tightness. In the process we introduce weak-tightness, a notion key to the results above and yielding some cardinal function results on monotonically normal...
Order-theoretical connectivity.