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 group invariants for one-dimensional spaces
We show that the Bruschlinsky group with the winding order is a homomorphism invariant for a class of one-dimensional inverse limit spaces. In particular we show that if a presentation of an inverse limit space satisfies the Simplicity Condition, then the Bruschlinsky group with the winding order of the inverse limit space is a dimension group and is a quotient of the dimension group with the standard order of the adjacency matrices associated with the presentation.
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
Ordering the local subsemigroups of a semigroup.
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.
Ordinal products of topological spaces
The notion of the ordinal product of a transfinite sequence of topological spaces which is an extension of the finite product operation is introduced. The dimensions of finite and infinite ordinal products are estimated. In particular, the dimensions of ordinary products of Smirnov's [S] and Henderson's [He1] compacta are calculated.
Paracompactness in ordered spaces
Paracompactness in the class of closed images of GO-spaces
Partial confluence of maps onto graphs and inverse limits of single graphs
Partial order and collapsibility of 2-complexes
Partially ordered sets with projections and their topology [Book]
Partitions of compact Hausdorff spaces
Under the assumption that the real line cannot be covered by -many nowhere dense sets, it is shown that (a) no Čech-complete space can be partitioned into -many closed nowhere dense sets; (b) no Hausdorff continuum can be partitioned into -many closed sets; and (c) no compact Hausdorff space can be partitioned into -many closed -sets.
Peano compactifications and property S metric spaces.