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ON THE MAZUR-ULAM THEOREM IN METRIC GROUPS
2009
Demonstratio Mathematica
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Let X, Y be abelian uniquely 2-divisible groups with metrics dx,dy respectively, invariant with respect to the translations and let there exist a constant c > 1 such that dy (2y, 0) > cdy{y, 0) for y € Y. We prove that each surjective isometry U : X -> Y has a form U(x) = a(x) + t/(0) for x 6 X, where a : X -• Y is a homomorphism. 1991 Mathematics Subject Classification: 46B99.
doi:10.1515/dema-2009-0112
fatcat:3m26ppjne5gl5o4x4tjfuvwkym