On the openness and discreteness of mappings with unbounded characteristic of quasiconformality |
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Authors: | E A Sevost’yanov |
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Institution: | 1.Institute of Applied Mathematics and Mechanics,Ukrainian National Academy of Sciences,Donetsk,Ukraine |
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Abstract: | The paper is devoted to the investigation of topological properties of space mappings. It is shown that orientation-preserving
mappings
f:D ?`(\mathbbRn)] f:D \to \overline {{\mathbb{R}^n}} in a domain
D ì \mathbbRn D \subset {\mathbb{R}^n} , n ≥ 2; which are more general than mappings with bounded distortion, are open and discrete if a function Q corresponding to the control of the distortion of families of curves under these mappings has slow growth in the domain f (D), e.g., if Q has finite mean oscillation at an arbitrary point y
0 ∈ f (D). |
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Keywords: | |
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