Order compatibility for Cauchy spaces and convergence spaces.
Order extension of order monomorphisms on a preordered topological space.
Order intervals in . Compactness, coincidence of topologies, metrizability
Let be a compact space and let be the Banach lattice of real-valued continuous functions on . We establish eleven conditions equivalent to the strong compactness of the order interval in , including the following ones: (i) consists of isolated points of ; (ii) is pointwise compact; (iii) is weakly compact; (iv) the strong topology and that of pointwise convergence coincide on ; (v) the strong and weak topologies coincide on . Moreover, the weak topology and that of pointwise convergence...
Order structures and topological structures
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 K-theoryand minimal symbolic dynamical systems
Recently a new invariant of K-theoretic nature has emerged which is potentially very useful for the study of symbolic systems. We give an outline of the theory behind this invariant. Then we demonstrate the relevance and power of the invariant, focusing on the families of substitution minimal systems and Toeplitz flows.
Ordered non-Archimedean fuzzy metric spaces and some fixed point results.
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 indices in Banach spaces.
Ordinal invariants and epimorphisms in some categories of weak Hausdorff spaces