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Title of Journal: Acta Math Hung

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Abbravation: Acta Mathematica Hungarica

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Springer Netherlands

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DOI

10.1007/s12307-014-0164-4

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1588-2632

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Weightable quasiuniformities

Authors: HansPeter A Künzi Salvador Romaguera
Publish Date: 2012/04/03
Volume: 136, Issue: 1-2, Pages: 107-128
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Abstract

The authors study quasiuniformities that are generated by a family of weightable quasipseudometrics Each totally bounded quasiuniformity is of this kind In some sense which is described in this article a weightable quasiuniformity is fairly symmetric with the associated weights generating small symmetrizersIn the second part of the article we continue our investigations by generalizing a subclass of weightable quasiuniformities to a more abstract level We introduce the concept of a tsymmetrizable quasiuniformity that is a quasiuniformity mathcalU possessing the property that there exists a totally bounded quasiuniformity mathcalZ such that mathcalUvee mathcalZ is a uniformity It turns out that tsymmetrizable quasiuniformities are closely related to quasiuniformities generated by weightable quasipseudometrics possessing bounded weight functions We show that several results that were originally proved for weightable quasipseudometrics with bounded weights still hold in a such apparently broader context

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Other Papers In This Journal:
  1. Rings of quotients of some infinite dimensional path algebras
  2. The Baum–Katz theorem for dependent sequences
  3. On complete convergence in mean for double sums of independent random elements in Banach spaces
  4. A note on the generalized rank reduction
  5. Existence and optimality of w -non-adjacent forms with an algebraic integer base
  6. Veldsman’s classes of associative rings
  7. Atomic decompositions of martingale hardy–morrey spaces
  8. A characterization of polyharmonic functions
  9. A note on invariant sets of iterated function systems
  10. On complete convergence and the strong law of large numbers for pairwise independent random variables
  11. Polynomial approximation with an exponential weight on the real semiaxis
  12. Best L 1 Approximation of Truncated Functions, Whitney-Type and Borh–Favard-Type Inequalities
  13. On the latticity of projection and antiprojection sets in Orlicz-Musielak spaces
  14. A categorical approach to absolute closure
  15. Planar zero divisor graphs of partially ordered sets
  16. On a problem in additive number theory
  17. On powers of relational and algebraic systems
  18. Inequalities for entire functions of exponential type satisfying $$ f(z) \equiv e^{i\gamma } e^{i\tau z} \overline {f(\bar z)} $$
  19. Local stability of a generalized Cauchy equation in Banach spaces
  20. A note on W - I -continuous functions
  21. A Remark on The Geometry of Spaces of Functions with Prime Frequencies
  22. Hua’s theorem with nine almost equal prime variables
  23. A weak type inequality for the maximal operator of ( C, α )-means of Fourier series with respect to the Walsh-Kaczmarz system
  24. Unification of generalized open sets on topological spaces
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