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Affinity of angle preserving mappings. (English. Russian original) Zbl 1030.51015
Mosc. Univ. Math. Bull. 57, No. 2, 41-43 (2002); translation from Vestn. Mosk. Univ., Ser. I 2002, No. 2, 60-63 (2002).
It is proved that the preservation of an angle (nonzero and nonstraight) is sufficient for a mapping $$\mathbb{R}^2\to \mathbb{R}^2$$ to be a similarity.
In terms of circle-preserving mappings a criterion is given for the fact that the mapping of an $$n$$-dimensional space into itself is a similarity.

##### MSC:
 51M05 Euclidean geometries (general) and generalizations 51N10 Affine analytic geometry