Uniformly finer topologies

We show that both the rationals (a σ-compact metric space) and the irrationals (a polish space) admit a topology, strictly finer than the euclidean at every point, such that the resulting spaces are homeomorphic to the original ones. An example with the same property is also given, where the metric space is complete and locally compact. However, if a topological space is both ?ech-complete and σ-compact, then this cannot happen.     

Uniformly primary ideals

This article introduces and advances the basic theory of “uniformly primary ideals” for commutative rings, a concept that imposes a certain boundedness condition on the usual notion of “primary ideal”. Characterizations of uniformly primary ideals are provided along with examples that give the theory independent value. Applications are also provided in contexts that are relevant to Noetherian rings.     

Uniformly 3-connected graphs

Let $k$ be a positive integer. A graph is said to be uniformly $k$-connected if between any pair of vertices the maximum number of independent paths is exactly $k$. Dawes showed that all minimally 3-connected graphs can be constructed from $K_4$ such that every graph in each intermediate step is also minimally 3-connected. In this paper, we generalize Dawes' result to uniformly 3-connected graphs. We give a constructive characterization of the class of uniformly 3-connected graphs which differs from the characterization provided by Göring et al., where their characterization requires the set of all 3-connected and 3-regular graphs as a starting set, the new characterization requires only the graph $K_4$. Eventually, we obtain a tight bound on the number of edges in uniformly 3-connected graphs.     

Uniformly differentiable bump functions

We present a construction of uniformly smooth norms from uniformly smooth bumb functions without making use of the Implicit Function Theorem.     

Uniformly Hyperarchimedean Lattice-Ordered Groups

An abelian ?-group with strong unit (\(\user1{\mathcal{L}}_1 \)-object) G is hyperarchimedean (HA) iff G?≤?C(YG) (the ?-group of real continuous functions on the maximal ideal space, YG) with λ(g)?=?inf{?∣?g(x)?∣?≠?0}?>?0 for each 0?≠?g?∈?G. In case inf{λ(g):0?≠?g?∈?G}?>?0, we call G uniformly hyperarchimedean (UHA). This paper: examines the structure of the UHA groups in detail; shows that UHA solves the problem: when is an \(\user1{\mathcal{L}}_1 \)-product HA?; describes completely the \(\user1{\mathcal{L}}_1 \)???HSP-classes which are contained in HA. Final remarks detail the connection with MV-algebras.     

Uniformly Classical Primary Submodules

We shall introduce the notion of uniformly classical primary submodule that generalizes the concept of uniformly primary ideal as given by J. A. Cox and A. J. Hetzel. We also advance the companion concepts of fully uniformly classical primary module and uniformly primary compatible module. Along these lines, we present a characterization of Noetherian rings R for which every R-module is fully uniformly classical primary and we present a characterization of rings R for which every finitely generated R-module is uniformly primary compatible. Results illustrating connections among the notions of uniformly classical primary submodule, uniformly primary ideal, and uniformly primary submodule as given by R. Ebrahimi-Atani and S. Ebrahimi-Atani are also provided.     

Uniformly cross intersecting families

Let A and B denote two families of subsets of an n-element set. The pair (A,B) is said to be ℓ-cross-intersecting iff |A∩B|=ℓ for all A∈ A and B∈B. Denote by P _e (n) the maximum value of |A||B| over all such pairs. The best known upper bound on P _e (n) is Θ(2 ⁿ ), by Frankl and R?dl. For a lower bound, Ahlswede, Cai and Zhang showed, for all n ≥ 2ℓ, a simple construction of an ℓ-cross-intersecting pair (A,B) with |A||B| = $ \left( {{*{20}c} {2\ell } \\ \ell \\ } \right) $ \left( {\begin{array}{*{20}c} {2\ell } \\ \ell \\ \end{array} } \right) 2 ^n−2ℓ = Θ(2 ⁿ /$ \sqrt \ell $ \sqrt \ell ), and conjectured that this is best possible. Consequently, Sgall asked whether or not P _e (n) decreases with ℓ.     

Algebraic-geometry codes, one-point codes, and evaluation codes

One-point codes are those algebraic-geometry codes for which the associated divisor is a non-negative multiple of a single point. Evaluation codes were defined in order to give an algebraic generalization of both one-point algebraic-geometry codes and Reed–Muller codes. Given an -algebra A, an order function on A and given a surjective -morphism of algebras , the ith evaluation code with respect to is defined as the code . In this work it is shown that under a certain hypothesis on the -algebra A, not only any evaluation code is a one-point code, but any sequence of evaluation codes is a sequence of one-point codes. This hypothesis on A is that its field of fractions is a function field over and that A is integrally closed. Moreover, we see that a sequence of algebraic-geometry codes G _i with associated divisors is the sequence of evaluation codes associated to some -algebra A, some order function and some surjective morphism with if and only if it is a sequence of one-point codes.      

Uniformly distributed sequences ofp-adic integers

Translated from Matematicheskie Zametki, Vol. 55, No. 2, pp. 3–46, February, 1994.     

Uniformly locally univalent harmonic mappings

The primary aim of this paper is to characterize the uniformly locally univalent harmonic mappings in the unit disk. Then, we obtain sharp distortion, growth and covering theorems for one parameter family \({{\mathcal {B}}}_{H}(\lambda )\) of uniformly locally univalent harmonic mappings. Finally, we show that the subclass of k-quasiconformal harmonic mappings in \({{\mathcal {B}}}_{H}(\lambda )\) and the class \({{\mathcal {B}}}_{H}(\lambda )\) are contained in the Hardy space of a specific exponent depending on \(\lambda \), respectively, and we also discuss the growth of coefficients for harmonic mappings in \({{\mathcal {B}}}_{H}(\lambda )\).     

Uniformly third-order accurate TVNE interpolations

In this paper, we develop an approximation procedure for functionsof bounded variations. Our procedure cannot increase the variationof the function being approximated, and also avoids discontinuityof the interpolation function.     

Uniformly separating families of functions

A concept concerning separation of points by functions is defined and studied. This concept has close relations with superpositions of functions and dimension theory, and these relations are investigated. A theorem concerning the dimension of projections of Cantor manifolds inR ^m is proved. This is a part of the authors Ph.D thesis prepared at the Hebrew University of Jerusalem under the supervision of Professor J. Lindenstrauss. The author wishes to thank Professor Lindenstrauss for his advice and encouragement during the preparation of this work.     

Uniformly maximumnorm stable difference schemes

Sufficient conditions for maximumnorm stability, uniform in the mesh-widths, of implicit two-level difference schemes with constant coefficients are given. Uniform stability is a necessary and sufficient condition for consistent difference schemes to be convergent, when the mesh-widths are unrelated.