Abstract
By the determination of all light-cone-preserving bijections of the plane K2, K an integral domain of a special kind, a big and striking contrast to the case of Kn (n ≥ 3) is exhibited (Theorem 1). Special regularity conditions are needed to single out all additive, continuous, K-linear, and Lorentz transformations of K2, respectively (Theorems 3, 4, 10). In the case that K is totally ordered, the preservance of a distance inequality (condition (M) in Theorem 7) plays a central role. For a further abstract, cf. [20].
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Dedicated to Professor Peter Wilker on his sixtieth birthday
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Rätz, J. (1983). On Light-Cone-Preserving Mappings of the Plane. In: Beckenbach, E.F., Walter, W. (eds) General Inequalities 3. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 64. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6290-5_27
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