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Periodica Mathematica Hungarica

, Volume 26, Issue 1, pp 77–84 | Cite as

Almost uniform convergence

  • J. Ewert
Article
  • 78 Downloads

Abstract

The almost uniform convergence is between uniform and quasi-uniform one. We give some necessary and sufficient conditions under which the almost uniform convergence coincides on compact sets with uniform, quasi-uniform or uniform convergence, respectively. In the second section continuity of almost uniform limits is considered. Finally we characterize the set of all points at which a net of functions is almost uniformly convergent to a given function.

Mathematics subject classification numbers, 1991

Primary 54A20 Key words and phrases Uniform convergence quasi-uniform convergence almost uniform convergence 

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References

  1. [1]
    R. F. Arens, A topology for spaces of transformations,Annals Math. 47 (1946), no. 3, 480–495.Google Scholar
  2. [2]
    R. Engelking,General Topology, Warszawa 1977.Google Scholar
  3. [3]
    M. Predoi, Sur la convergence quasi-uniforme,Period. Math. Hungarica 10 (1979), 31–40.Google Scholar

Copyright information

© Akadémiai Kiadó 1993

Authors and Affiliations

  • J. Ewert
    • 1
  1. 1.Mathematical InstituteUniversity of WroclawWroclawPoland

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