Uniform AR's and ANR's
Uniform convergence on spaces of multifunctions
Uniform density and m-density for subrings of C(X).
Uniform limits of Darboux functions on the Euclidean plane
Uniform maps into normed spaces
Thirteen properties of uniform spaces are shown to be equivalent. The most important properties seem to be those related to modules of uniformly continuous mappings into normed spaces, and to partitions of unity.
Uniform sequences of -mappings
Uniform shape and uniform Čech homology and cohomology groups for metric spaces
Uniform weight of uniform quotients
Uniforme Räume mit einer linear geordneten Basis.
Uniformities, Hyperspaces, and Normality.
Uniformity and classes of real valued function system
Uniformly continuous selections
Uniformly Movable Categories and Uniform Movability of Topological Spaces
A categorical generalization of the notion of movability from inverse systems and shape theory was given by the first author who defined the notion of movable category and used it to interpret the movability of topological spaces. In this paper the authors define the notion of uniformly movable category and prove that a topological space is uniformly movable in the sense of shape theory if and only if its comma category in the homotopy category HTop over the subcategory HPol of polyhedra is uniformly...
Unique -closure for some -groups of rational valued functions
Usually, an abelian -group, even an archimedean -group, has a relatively large infinity of distinct -closures. Here, we find a reasonably large class with unique and perfectly describable -closure, the class of archimedean -groups with weak unit which are “-convex”. ( is the group of rationals.) Any is -convex and its unique -closure is the Alexandroff algebra of functions on defined from the clopen sets; this is sometimes .
Uniqueness and non uniqueness of optimal maps in mass transport problem with not strictly convex cost
In the setting of the optimal transportation problem we provide some conditions which ensure the existence and the uniqueness of the optimal map in the case of cost functions satisfying mild regularity hypothesis and no convexity or concavity assumptions.
Uniqueness of Representation Spaces.
Unitary sequences and classes of barrelledness.
It is well known that some dense subspaces of a barrelled space could be not barrelled. Here we prove that dense subspaces of l∞ (Ω, X) are barrelled (unordered Baire-like or p?barrelled) spaces if they have ?enough? subspaces with the considered barrelledness property and if the normed space X has this barrelledness property.These dense subspaces are used in measure theory and its barrelledness is related with some sequences of unitary vectors.
Universal completely regular dendrites
We define a dendrite which is universal in the class of all completely regular dendrites with order of points not greater than n. In particular, the dendrite is universal in the class of all completely regular dendrites. The construction starts with the standard universal dendrite of order n described by J. J. Charatonik.
Universal images of universal elements
We furnish several necessary and sufficient conditions for the following property: For a topological space X, a continuous selfmapping S of X and a family τ of continuous selfmappings of X, the image under S of every τ-universal element is also τ-universal. An application in operator theory, where we extend results of Bourdon, Herrero, Bes, Herzog and Lemmert, is given. In particular, it is proved that every hypercyclic operator on a real or complex Banach space has a dense invariant linear manifold...
Universal mappings and weakly confluent mappings