Uniformities, Hyperspaces, and Normality.
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...
Variations of uniform completeness related to realcompactness
Various characterizations of realcompactness are transferred to uniform spaces giving non-equivalent concepts. Their properties, relations and characterizations are described in this paper. A Shirota-like characterization of certain uniform realcompactness proved by Garrido and Meroño for metrizable spaces is generalized to uniform spaces. The paper may be considered as a unifying survey of known results with some new results added.
Vervollständigung streng ausgeglichener Limesvektorräume I.
Vervollständigung streng ausgeglichener Limesvektorräume II.
Weak Compatibility and Common Fixed Point Theorems for A-Contractive and E-expansive Maps in Uniform Spaces
2000 Mathematics Subject Classification: 47H10, 54E15.The purpose of this paper is to define the notion of A-distance and E-distance in uniform spaces and give several new common fixed point results for weakly compatible contractive or expansive selfmappings of uniform spaces.
Weak-open compact images of metric spaces
The main results of this paper are that (1) a space is -developable if and only if it is a weak-open image of a metric space, one consequence of the result being the correction of an error in the paper of Z. Li and S. Lin; (2) characterizations of weak-open compact images of metric spaces, which is another answer to a question in in the paper of Y. Ikeda, C. liu and Y. Tanaka.
Weil nearness spaces.
Weil uniformities for frames
In pointfree topology, the notion of uniformity in the form of a system of covers was introduced by J. Isbell in [11], and later developed by A. Pultr in [14] and [15]. Another equivalent notion of locale uniformity was given by P. Fletcher and W. Hunsaker in [6], which they called “entourage uniformity”. The purpose of this paper is to formulate and investigate an alternative definition of entourage uniformity which is more likely to the Weil pointed entourage uniformity, since it is expressed...
Wellchainedness characterizations of connected relators.