Uniform quotient mappings of the plane with non-discrete point inverses
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.
KeywordsUniform Continuity Uniform Limit Null Sequence Monotone Open Mapping Good Modulus
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- [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
- [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