Israel Journal of Mathematics

, Volume 124, Issue 1, pp 203–213 | Cite as

Uniform quotient mappings of the plane with non-discrete point inverses

  • Aicke Hinrichs


We construct uniform quotient mappings of the plane which have points with non-discrete inverse and good modulus of continuity. In particular, we find a monotone uniform quotient mappingf: ℝ2 → ℝ2 having a point with nontrivial inverse such that lim r→0[Ω(r)/r γ]=0 for anyγ<1/2, where Ω is the modulus of continuity off.


Uniform Continuity Uniform Limit Null Sequence Monotone Open Mapping Good Modulus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [And]
    R. D. Anderson,On monotone interior mappings in the plane, Transactions of the American Mathematical Society73 (1952), 211–222.MATHCrossRefMathSciNetGoogle Scholar
  2. [BJLPS]
    S. M. Bates, W. B. Johnson, J. Lindenstrauss, D. Preiss and G. Schechtman,Affine approximation of Lipschitz functions and nonlinear quotients, Geometric and Functional Analysis, to appear.Google Scholar
  3. [JLPS]
    W. B. Johnson, J. Lindenstrauss, D. Preiss and G. Schechtman,Uniform quotient mappings of the plane, The Michigan Mathematical Journal, to appear.Google Scholar
  4. [LW]
    W. Lewis and J. J. Walsh,A continuous decomposition of the plane into pseudo-arcs, Houston Journal of Mathematics4 (1978), 209–222.MATHMathSciNetGoogle Scholar
  5. [Sea]
    C. R. Seaquist,A new continuous cellular decomposition of the disk into non-degenerate elements, Topology Proceedings19 (1994), 249–276.MATHMathSciNetGoogle Scholar
  6. [Why]
    G. T. Whyburn,Analytic Topology, American Mathematical Society, New York, 1942.MATHGoogle Scholar

Copyright information

© The Hebrew University Magnes Press 2001

Authors and Affiliations

  1. 1.Mathematisches Institut, FSU JenaJenaGermany

Personalised recommendations