Uniform quotients of metric spaces
Uniform quotients of metrizable spaces
Uniform regularity of measures on locally compact spaces.
Uniform shape and uniform Čech homology and cohomology groups for metric spaces
Uniform Space
In this article, we formalize in Mizar [1] the notion of uniform space introduced by André Weil using the concepts of entourages [2]. We present some results between uniform space and pseudo metric space. We introduce the concepts of left-uniformity and right-uniformity of a topological group. Next, we define the concept of the partition topology. Following the Vlach’s works [11, 10], we define the semi-uniform space induced by a tolerance and the uniform space induced by an equivalence relation....
Uniform spaces with easy behavior with respect to coreflections
Uniform topology onEQ-algebras
In this paper, we use filters of an EQ-algebra E to induce a uniform structure (E, 𝓚), and then the part 𝓚 induce a uniform topology 𝒯 in E. We prove that the pair (E, 𝒯) is a topological EQ-algebra, and some properties of (E, 𝒯) are investigated. In particular, we show that (E, 𝒯) is a first-countable, zero-dimensional, disconnected and completely regular space. Finally, by using convergence of nets, the convergence of topological EQ-algebras is obtained.
Uniform weight of uniform quotients
Uniforme Räume mit einer linear geordneten Basis.
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 Convex Metric Spaces
In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology, called coconvex topology, agrees with the usually weak topology in Banach spaces. An example of a CAT(0)-space with weak topology which is not Hausdorff is given. In the end existence and uniqueness...
Uniformly convex spaces, bead spaces, and equivalence conditions
The notion of a metric bead space was introduced in the preceding paper (L. Pasicki: Bead spaces and fixed point theorems, Topology Appl., vol. 156 (2009), 1811–1816) and it was proved there that every bounded set in such a space (provided the space is complete) has a unique central point. The bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces. It appears that normed bead spaces are identical with uniformly convex spaces. On the...