Uniform quotient mappings of the plane with non-discrete point inverses |
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| Authors: | Aicke Hinrichs |
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| Institution: | (1) Mathematisches Institut, FSU Jena, D 07743 Jena, Germany;(2) Present address: Department of Mathematics, Texas A&M University, 77843 College Station, TX, USA |
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| Abstract: | 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→0Ω(r)/r
γ]=0 for anyγ<1/2, where Ω is the modulus of continuity off.
Supported by DFG grant Hi 584/2-1. |
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