Uniformities obtained from filter spaces
Uniformizable Cauchy spaces.
Uniformization and anti-uniformization properties of ladder systems
Natural weakenings of uniformizability of a ladder system on ω₁ are considered. It is shown that even assuming CH all the properties may be distinct in a strong sense. In addition, these properties are studied in conjunction with other properties inconsistent with full uniformizability, which we call anti-uniformization properties. The most important conjunction considered is the uniformization property we call countable metacompactness and the anti-uniformization property we call thinness. The...
Uniformization of Convergence Spaces. Part I. Definitions and Fundamental Constructions.
Uniformization of Convergence Spaces Part II: Conjugate Convergence Structures and Bi-Structures.
Uniformization of Neighborhood Axioms.
Uniformization of Topological Spaces with Small Inductive Dimension Zero.
Uniformly continuous selections
Uniformly, proximally and topologically compact relators.
Universal metric spaces
Upper and Lower Bounds in Relator Spaces
2000 Mathematics Subject Classification: 06A06, 54E15An ordered pair X(R) = ( X, R ) consisting of a nonvoid set X and a nonvoid family R of binary relations on X is called a relator space. Relator spaces are straightforward generalizations not only of uniform spaces, but also of ordered sets. Therefore, in a relator space we can naturally define not only some topological notions, but also some order theoretic ones. It turns out that these two, apparently quite different, types of notions are closely...