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.
Paracompactness in ordered spaces
Paracompactness in the class of closed images of GO-spaces
Partial order and collapsibility of 2-complexes
Partially ordered sets with projections and their topology [Book]
Polouspořádané lineární prostory
Pressing Down Lemma for -trees and its applications
For any ordinal of uncountable cofinality, a -tree is a tree of height such that for each , where . In this note we get a Pressing Down Lemma for -trees and discuss some of its applications. We show that if is an uncountable ordinal and is a Hausdorff tree of height such that for each , then the tree is collectionwise Hausdorff if and only if for each antichain and for each limit ordinal with , is not stationary in . In the last part of this note, we investigate some...
Primitive words and spectral spaces.
Problems 44 and 39 on compact semilattices.
Profinite relational structures
Property Q.
Quasi-metrization and hereditary normality of compact bitopological spaces
Quasi-pseudometrizability of the point open ordered spaces and the compact open ordered spaces.
Quasi-uniform completions of partially ordered spaces
Random periodic point and fixed point results for random monotone mappings in ordered Polish spaces.