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Remarks on Efimov’s theorem about differential tests of homeomorphism. (English) Zbl 0758.58006
The main result: If a $$C^ 1$$-mapping $$f$$ of the plane into the plane satisfies conditions similar to the ones of known Efimov’s theorem [N. V. Efimov, Mat. Sb., n. Ser. 76(118), 499-512 (1968; Zbl 0164.215)], then $$f$$ is a diffeomorphism and $$f(\mathbb{R}^ 2)=\mathbb{R}^ 2$$.

##### MSC:
 58C25 Differentiable maps on manifolds